CURRICULUM VITAE

Name : SUBHASHISH BANERJEE

Sex : Male

Address for Correspondence:

Subhashish Banerjee

Indian Institute of Technology Jodhpur,

NH 62, Nagaur Road , Karwar, Jodhpur-342037

Email : subhashish@iitj.ac.in; subhashishb05@gmail.com.

Homepage: http://home.iitj.ac.in/ subhashish/

1. Academic Records:

(a) Bachelor of Engineering (B.E.) 1996, Delhi College of Engineering, Delhi Univer-

sity, New Delhi, India.

(b) Ph.D obtained in August 2003, School of Physical Sciences, J.N.U., New Delhi,

India.

Thesis Title:

“Study of Dynamics of Open Quantum Systems using the Functional Integral Approach.”

Thesis Supervisor:

Prof. R. Ghosh, School of Physical Sciences, J.N.U.

Research and Teaching Experience:

1. Postdoctoral Position:

(a) Postdoctoral Position: From February 2004 till April 2005 in Fachbereich

Physik, Kaiserslautern (Germany). Postdoctral Supervisor: Prof. Dr. Joachim

Kupsch.

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(b) Postdoctoral Visitor: June, July 2005 in Centre for High Energy Physics

(CHEP), Indian Institute of Science (IISc), Bangalore (India).

(c) Postdoctoral Position: From September 2005 to July 2008, in the Theoretical

Physics Group, Raman Research Institute, Bangalore (India).

2. Faculty Position:

(a) From August 2008-March 2010 at Chennai Mathematical Institute, Siruseri, Chen-

nai, India: Visiting Fellow;

(b) From April 2010- June 2010 at Chennai Mathematical Institute, Siruseri, Chennai,

India: Asst. Prof.;

(c) From July 2010 - March 26, 2019 at Indian Institute of Technology Rajasthan,

Jodhpur, India: Asst. Prof;

(d) From 27/03/2019 to present, Indian Institute of Technology Rajasthan, Jodhpur,

India: Associate Professor.

3. Teaching Experience:

(a) Course instructor at Indian Institute of Technology Rajasthan:

i. Physics-I (Ist Semester, Undergraduate B.E.): This course consists of the

elements of electrostatics, electrodynamics as well as the nature of these laws

in, say, a dielectric medium. Then the elements of special theory of relativity

are covered, followed by an introduction to quantum mechanics. The idea is

to provide the students with a basic understanding of the need for quantum

mechanics, at an early stage. Thus the basic idea of wave-particle duality

is stressed and is supplemented with discussions of the photoelectric and

Compton effect. (Taught again, as a shared course, in July-Nov. 2019.)

ii. Physics-II (IInd Semester, Undergraduate B.E.): This course deals with

an amalgamation of statistical mechanics and solid state physics. The ba-

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sic ideas of X-ray diffraction are discussed followed by some basic concepts

in equilibrium statistical mechanics, with a stress on the various statistical

distributions existing in nature; the emphasis being on the Fermi-Dirac dis-

tributions. This is followed by a discussion of free Fermi gas, band theory. All

this is then put to use to understand metals, semi-conductors and insulators.

In semi-conductors, the p-n junction is discussed thoroughly, and is used to

discuss devices such as Zener diodes, transistors, photovoltaic diodes or solar

cells.

iii. Undergraduate Physics Laboratory (Ist Semester, Undergraduate B.E.):

Involved in the running of the undergraduate physics laboratory in the first

semester: which involved experiments related to mechanics, electromagnetism,

optics. Some of the experiments performed were:

Stationary waves in string; verification of Newton’s Second Law; moment

of inertia of a bicycle wheel; determination of e/m ration; interference and

diffraction of light; refractive index of a prism; magnetic forces on wires;

Faraday’s law of induction.

iv. Physics-III (IIIrd Semester, Undergraduate B.E.): Developed and taught

the course Physics-III, containing Newtonian Mechanics, Rotational Dynam-

ics, Special Theory of Relativity, Motion Under Central Forces, and an In-

troduction to Non-Linear Dynamics where concepts such as Fixed points,

stability; determination of fixed points; limit cycles; periodic conditions and

linear maps; chaotic motion and non-linear maps are discussed.

v. Quantum Mechanics and Its Applications (IVth Semester, Undergradu-

ate B.E.): introducing quantum mechanics to undergraduate students. Basic

experiments, concepts and a brief glimpse of some of its modern applications

such as quantum optics and information, nuclear and particle physics.

vi. Quantum Mechanics Laboratory (IVth Semester, Undergraduate B.E.):

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basic ideas of quantum mechanics illustrated via the Franck Hertz experiment,

e/m ratio, B−H curve, photoelectric effect, band gap of semiconductors and

optics experiments such as diffraction grating.

vii. Nature and Properties of Materials Laboratory (IInd Semester, Un-

dergraduate B.E.):

This lab course aims at providing a glimpse to the students of various aspects

of material properties of systems, such as thermal, optical and mechanical

properties, some of which they have already studies in their Physics-II course.

viii. Introduction to Quantum Computation and Information: designed

and taught this course, consisting of an Introduction to Quantum Mechanics,

Quantum Computation, Classical Information and Communication, Quan-

tum Information, Entanglement, Quantum Communication and some appli-

cations, such as Quantum copying, deletionand quantum cryptography.

ix. Introduction to System Science and Dynamics: course on Systems

Science for M.Tech. and Ph.D. students. We highlight the ubiquitousness of

the systems philosophy, by applications to concrete systems such as spring

systems. These systems are prototypes of systems modelling, as they occur in

the physical sciences as well as in numerous engineering applications, such as

in Electric Circuit Theory. We then discuss the fundamental concepts of self-

organization and synergetics with examples drawn from problems in physics,

biology and sociology.

x. Introduction to Cryptography and Coding: Here we introduce the ba-

sic concepts of cryptography and coding, classical as well as quantum. This

is a course for Post Graduate Students as well as interested final year under-

graduate students.

xi. Information Theory and Probability: for Postgraduate students;

xii. Relativistic Quantum Mechanics: Quantum mechanics in the relativistic

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regime, for graduate students. The course consists of discussions of relativistic

wave equations, Maxwell, Klein-Gordan and Dirac. Also discussed are the

concepts of symmetry in the relativistic regime.

xiii. Quantum Field Theory: an introductory course on quantum field theory

for graduate students. The course deals with Noether’s theorem, canonical

quantization of free and interacting field theories such as Klein-Gordan, Dirac

and Maxwell theory.

xiv. Critical Phenomena and Renormalization Group: Basic concepts of

scaling and renormalization group in critical phenomena for MSc and PhD

students.

xv. Quantum Mechanics: an introduction of quantum mechanics to MSc (Mas-

ters in Science) students. The course covers postulates of quantum mechanics,

uncertainty principle, time-independent perturbation theory, harmonic oscil-

lators, angular momentum and the Hydrogen atom.

xvi. Statistical Mechanics: basic thermodynamics and statistical mechanics for

MSc students;

xvii. Atomic and Nuclear Physics: introduction to atomic and nuclear physics

for MSc students;

xviii. Electrodynamics: Basic electrodynamics, with an introduction to relativis-

tic effects and optics, for masters students (MSc Physics);

xix. Classical Mechanics: Basic classical mechanics for for masters students

(MSc Physics);

xx. Basic Physics: an elementary introduction to modern aspects of physics

such as quantum mechanics, atomic and nuclear physics, special relativity,

lasers and superconductivity to BSc (Bachelor of Science) students at NLU

(National Law University) Jodhpur, India.

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(b) Course instructor at Chennai Mathematical Institute for:

i. Newtonian Mechanics: This course deals with Newtonian mechanics and

its consequences. The emphasis here is in an appreciation of the inherent

conservation laws that form the basis of the phenomena studied. Also, wher-

ever possible, experiments are discussed. For e.g., the beautiful experiment

performed by I. Estermann et al.: Phys. Rev. A: 71, 238 (1947), to test the

theoretical velocity distribution of atoms at a given temperature making use

of Newtonian mechanics to the free fall of individual atoms;

ii. Statistical Mechanics-I: Thermodynamics: Thermodynamics is a re-

markably successful theory about the macroscopic world. This course deals

with spelling out the phenomenological origin of thermodynamics, in partic-

ular equilibrium thermodynamics and studying its various consequences;

iii. Statistical Mechanics-II: Here we deal with the microscopic theory un-

derlying the macroscopic manifestations of thermodynamics. This course is

about equilibrium phenomena. The concept of ensembles in classical statis-

tical mechanics is developed in length and the program is carried forward

to quantum statistical mechanics. This is then applied to a number of phe-

nomena such as magnetism, black body radiation, theory of solids and Bose-

Einstein condensation.

iv. Statistical Mechanics-III: Ising model, phase transition, elements of non-

equilibrium statistical mechanics.

(c) Teaching experience during PhD and Post-Doctoral period:

i. Teaching assistant for courses in electromagnetic theory, quantum mechanics

and quantum field theory in J.N.U., New Delhi.

ii. Teaching assistant for courses in quantum mechanics and statistical mechanics

in Fachbereich Physik, Kaiserslautern.

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Conferences Attended:

1. International Conference on “Recent Developments in Theoretical Physics”, T.I.F.R.,

Mumbai, January 1999.

2. International Conference on “Foundations of Quantum Mechanics and Quantum Op-

tics”, S. N. Bose Centre, Calcutta, January 2000.

3. SERC School 2000 on “Field Theories in Condensed Matter Systems”, M.R.I. Alla-

habad, February 2000.

4. International Symposium on “Entanglement, Information and Noise”, June 14-20,

2004 in Krzyzowa, Poland. Presented a poster on “Decoherence and Dissipation of an Open

Quantum System with a Squeezed and Frequency-Modulated heat bath”.

5. 330th WE-Heraeus Seminar on “Controlling Decoherence”, July 26-28, 2004 in Bad

Honnef, Germany. Presented a poster on “The effect of Squeezing of the Bath on the

Decoherence and Dissipation properties of an Open Quantum System”.

6. D.I.C.E. 2004 on “From Decoherence and Emergent Classicality to Emergent Quantum

Mechanics”, September 1-4, 2004 in (Castello di) Piombino, Italy.

7. Non-Equilibrium Phenomena: Tenth Discussion Meeting in a Frontier Area of Re-

search; January 2006, Bangalore, India.

8. Entanglement in Quantum Condensed Matter Systems: 17-29 November, 2008, at

Institute of Mathematical Sciences, Chennai, India.

9. “International Program on Quantum Information (IPQI)” held at Institute of Physics

(IOP), Bhubaneswar, Orissa, India: January 4th-30th, 2010.

10. “ International Conference on Quantum Optics and Quantum Computing (ICQOQC-

11): March 24-26, 2011; organized by the Department of Physics and Materials Science and

Engineering, Jaypee Institute of Information Technology, Noida, India.

11. “International Program on Quantum Information (IPQI) 2011” held at Institute of

Physics (IOP), Bhubaneswar, Orissa, India from December 13th-22nd, 2011.

12. “International Workshop on Quantum Information (IWQI) 2012” held at Harish

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Chandra Research Institute (HRI), Allahabad, India from January 20th-26th, 2012.

13. “8th Nalanda Dialog on Science and Philosophy” held at Nava Nalanda Mahavihara,

Nalanda, Bihar from January 21-24, 2013.

Seminars Presented at:

1. School of Physical Sciences, Jawaharlal Nehru University, New Delhi, India.

2. University of Kaiserslautern, Germany.

3. University of Augsburg, Germany.

4. University of Cologne, Germany.

5. Centre for High Energy Physics, Indian Institute of Science, Bangalore, India.

6. Indian Institute of Astrophysics, Bangalore, India.

7. Raman Research Institute, Bangalore, India.

8. Indian Institute of Technology, Kanpur, India.

9. Chennai Mathematical Institute, Chennai, India.

10. Institute of Mathematical Sciences, Chennai, India.

11. Institute of Physics, Bhubaneswar, India.

12. Harish-Chandra Research Institute, Allahabad, India.

13. Indian Statistical Institute (ISI), Kolkata.

14. Cultivation of Science, Kolkata.

15. Department of Physics and Materials Science and Engineering, Jaypee Institute of

Information Technology, Noida, India.

16. University of Freiburg, Freiburg, Germany (June, 2017). Title of Talk “Aspects Of

Non-Markovianity in Quantum Walks”.

17. Institute for Theoretical Physics, TU Wein (June, 2017). Title of Talk “Aspects Of

Non-Markovianity in Quantum Walks”.

18. University of Technology of Troyes (UTT), France (June, 2017). Title of Talk “An

Invitation to Open Quantum Systems and Quantum Cryptography”.

19. IMSc Workshop on Quantum Metrology and Open Quantum Systems, August 26-31,

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2018, Kodaikanal Solar Observatory. Title of talk “Open Quantum Systems and Quantum

Information in Relativistic and Sub-atomic Systems”.

20. University of Turku, Finland (June 12, 2019). Title of talk “Open Quantum Systems:

Non-Markovian Phenomena”.

21. Colloquium at IISc Bangalore, India (November 15, 2019). Title of talk “Open

Quantum Systems and Quantum Information in Relativistic and Sub-atomic Systems: An

Introduction”.

Outreach:

1. Was an active participant in: (a) Workshop on Systems Science - Complex Networks

and Applications, May 07-09, 2012;

(b) International Workshop on Quantum Biology, January 25-27, 2013;

(c) International Workshop on Computational Materials Design and Engineering, Febru-

ary 8-10, 2013;

held at Indian Institute of Technology Jodhpur.

2. Convener of International Meet on Quantum Correlations and Logic, Language and

Set Theory 2013, at Indian Institute of Technology Jodhpur from December 9 to 14, 2013.

3. Course Coordinator of GIAN programme 171009M01 Topological Solitons and their

Applications, from December 10-15, 2018 at IIT Jodhpur. External faculty was Prof. Richard

MacKenzie of University of Montreal, Canada.

4. Invited speaker to sixteen international conferences on Quantum Information.

5. Invited speaker to the 8th Nalanda Dialog on Science and Philosophy held at Nava

Nalanda Mahavihara, Nalanda, Bihar, India from January 21-24, 2013.

6. Keynote speaker at the “One-Day Workshop on Quantum Communications” at

Malviya National Institute of Technology (MNIT) Jaipur in September 2016.

7. Coordinator of Faculty Development Proghram (FDP) on Quantum Science and Tech-

nology from August 19 to 30, 2019, at IIT Jodhpur.

8. Coordinator and Convenor of Conference on Quantum Information and Computation:

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QIC-2019, at Indian Institute of Technology Jodhpur from December 8 to 11, 2019.

9. As the first Head of the Physics Department at IIT Jodhpur, helped to develop the

MSc Physics program introduced in July 2015. This involved, among other things, devel-

opment of the courses and getting them approved from an external committee of senior

Physicsts from the various IITs and TIFR (Mumbai).

Invited Speaker at National and International Conferences:

1. Invited speaker to the “Symposium on Quantum Information”, 16-17 March, 2007 at

School of Physical Sciences, Jawaharlal Nehru University, N. Delhi. Title of talk: “Deco-

herence without dissipation and its applications to Quantum Computation”.

2. Invited speaker in “Entanglement in Quantum Condensed Matter Systems” : 17-

29 November, 2008 at Institute of Mathematical Sciences, Chennai, India. Title of talk:

“Open Quantum Systems”.

3. Invited speaker in “International Program on Quantum Information (IPQI)” held at

Institute of Physics (IOP), Bhubaneswar, Orissa, India from January 4th-30th, 2010. Title

of talk: “Dynamics of Entanglement in Open Quantum Systems”.

4. Invited speaker in “ International Conference on Quantum Optics and Quantum

Computing (ICQOQC-11): March 24-26, 2011; organized by the Department of Physics

and Materials Science and Engineering, Jaypee Institute of Information Technology, Noida,

India. Title of talk: “Effect of Control Procedures on Entanglement Evolution in Open

Quantum Systems”.

5. Invited speaker in “International Program on Quantum Information (IPQI) 2011”

held at Institute of Physics (IOP), Bhubaneswar, Orissa, India from December 13th-22nd,

2011. Title of talk: “Dynamics of Quantum Correlations in Open Quantum Systems”.

6. Invited speaker in “International Workshop on Quantum Information (IWQI) 2012”

held at Harish Chandra Research Institute (HRI), Allahabad, India from January 20th-26th,

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2012. Title of talk: “Aspects of Open Quantum Systems in Quantum Information”.

7. Invited speaker in “8th Nalanda Dialog on Science and Philosophy” held at Nava

Nalanda Mahavihara, Nalanda, Bihar from January 21-24, 2013.

8. Invited speaker in “International Workshop in Optical Quantum Information” Septem-

ber 01-2, 2013; organized by the Department of Physics and Materials Science and Engineer-

ing, Jaypee Institute of Information Technology, Noida, India. Title of talk: “A Journey

from Quantum Optics to Quantum Information”.

9. Invited speaker in “Meeting on Quantum Information Processing and Applications

(QIPA-2013)”: December 02-08, 2013 at Harish-Chandra Research Institute (HRI), Alla-

habad, India. Title of talk: “Quantum Information: From the perspective of Quantum

Optics”.

10. Invited speaker in “National Conference on Quantum Correlations: Foundations and

Applications” from March 04-05, 2014; organized by Department of Physics, Vidyasagar

College for Women, Kolkata along with Physics and Applied Mathematics Unit, Indian

Statistical Institute, Kolkata. Title of talk: “An Invitation to Open Quantum Systems

Applied to Quantum Information”.

11. Invited speaker in “School and Discussion Meeting Frontiers In Light-Matter Inter-

actions” December 08-22, 2014 at Cultivation of Science, Kolkata and organized by ICTS,

Bangalore. Title of talk: “An Invitation to Open Quantum Systems: A Density Matrix

Approach”.

12. Invited speaker in “International Conference on Quantum Foundations (ICQF15)”

November 30- December 04, 2015 organized by NIT, Patna. Title of talk: “Quasidistribu-

tions and Tomograms in Open Quantum Systems”.

13. Invited speaker in “Meeting on Quantum Information Processing and Applications

(QIPA-2015)” December 07-13, 2015 at Harish-Chandra Research Institute (HRI), Alla-

habad, India. Title of talk: “Open Quantum Systems and Quantum Information in Rela-

tivistic and Sub-atomic Systems”.

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14. Invited speaker in “International Conference on Quantum Foundations (ICQF17)”

December 04- 09, 2017, organized by NIT, Patna. Title of talk: “Aspects Of NonMarko-

vianity In Quantum Walks”.

15. Invited speaker in “International Symposium on New Frontiers in Quantum Cor-

relations (ISNFQC18)”, January 29- February 03, 2018, organized by S N Bose Centre for

Fundamental Sciences, Kolkata. Title of talk: “Open Quantum Systems and Quantum

Information in Sub-atomic Systems”.

16. Invited speaker in “Workshop on Quantum Metrology and Open Quantum Systems”,

August 26-31, 2018, Kodaikanal Solar Observatory, organized by IMSc, Chennai. Title of

talk: “Open Quantum Systems and Quantum Information in Relativistic and Sub-atomic

Systems.”

Invited Reviewer:

1. Invited reviewer for Mathematical Reviews (MR) (a division of the American Mathe-

matical Society). Reviewed the papers:

a. “Dynamics of pairwise entanglement between two Tavis-Cummings atoms” by J-L.

Guo and H-S. Song. Journal ref.: Jr. of Phys. A: Math. Theor. 41, 085302 (2008);

b. “ Environment-invariant measure of distance between evolutions of an open quantum

system” by M. D. Grace; J. Dominy; R. L. Kosut; C. Brif and H. Rabitz. Journal ref.: New

Journal of Physics 12, 015001 (2010); Review Number: MR2581170;

c. “ Maps for general open quantum systems and a theory of linear quantum error

correction” by A. Shabani and D. A. Lidar. Journal Ref.: Phys. Rev. A 80, 012309 (2009);

Review Number: MR2580789;

d. “Coherent states for a polynomial su(1, 1) algebra and a conditionally solvable system”

by M. Sadiq; A. Inomata; G. Junker. Journal Ref.: J. Phys. A 42, 365210 (2009); Review

Number: MR2534518;

e. “A Quantum Coupler and the Harmonic Oscillator Interacting with a Reservoir:

Defining the Relative Phase Gate” by P. C. Garcia Quijas and L. M. AreValo Aguilar.

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Journal Ref.: Quantum Information and Computation 10 190 (2010); Review Number:

MR2649358;

f. “Position-dependent mass oscillators and coherent states” by S. Cruz y Cruz; O.

Rosas-Ortiz. Journal Ref.: J. Phys. A 42, 185205 (2009); Review Number: MR2591199;

g. “The rotating-wave approximation: consistency and applicability from an open quan-

tum system analysis” by C. Fleming; N. I. Cummings; C. Anastopoulos and B L Hu. Journal

Ref.: J. Phys. A 43, 405304 (2010); Review Number: MR2740391.

h. “Complex WKB evolution of Markovian Open Systems” by O. Brodier and A. M.

Ozorio de Almeida. Journal Ref.: J. Phys. A:Math. Theor. 43 505308, (2010); Review

Number: MR2725563.

i. “Stabilizing Quantum States by Constructive Design of Open Quantum Dynamics” by

F. Ticozzi; S. G. Schirmer and X. Wang. Journal Ref.: IEEE Transcations On Automatic

Control 55 2901 (2010); Review Number: MR2767162.

j. “Quantum Memories as Open Systems ” by Robert Alicki. Journal Ref.: Mathematical

Horizons for Quantum Physics, 97-108, Lect. Notes Ser. Inst. Math. Sci. Natl. Univ.

Singap., 20, World Sci. Publ., Hackensack, NJ, 2010; Review Number: MR2731890.

k. “Open Quantum Systems In Non-Inertial Frames” by S. Khan; M. K. Khan. Journal

Ref.: J. Phys. A 44 045305 (2011); Review Number: MR2754724.

l. “Quantum Open Systems with Time-Dependent Control” by Robert Alicki. Journal

Ref.: Lect. Notes Phys. 787, 79 (2010); Review Number: MR2762153.

m. “ Exact solutions for a family of spin-boson systems” by Yuan-Harng Lee, Jon

Links and Yao-Zhong Zhang, Journal Ref: Nonlinearity 24 1975 (2011); Review Number:

MR2805589.

n. “Shell Model for Open Quantum Systems” by M. Ploszajczak and J. Okolowicz.

Journal Ref.: Int J Theor Phys. 50 1097 (2011); Review Number: MR2780950.

o. “ Resonant-state Expansion of the Green’s Function of Open Quantum Systems” by

Naomichi Hatano and Gonzalo Ordonez. Journal Reference: Int J Theor Phys. 50 1105

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(2011); Review Number: MR2780951.

p. “A new kind of geometric phases in open quantum systems and higher gauge theory”

by David Viennot and Jose Lages. Journal Reference: J. Phys. A: Math. Theor. 44 365301

(2011); Review Number: MR2826547.

q. “New Approach for Solving the Lindblad Equation of the Density Operator for a

Harmonic Oscillator Interacting with an Electromagnetic Field” by Jun Zhou, Hong-Yi Fan

and Jun Song. Journal Reference: Int. J. Thor. Phys. 50 3149 (2011); Review Number:

MR2833198.

r. “Volume fractions of the kinematic ‘near-critical’ sets of the quantum ensemble control

landscape” by Jason Dominy and Herschel Rabitz. Journal Reference: J. Phys. A: Math.

Theor. 44 255302 (2011); Review Number: MR2800875.

s. “ Wigner Function of a Special Type of Squeezed Coherent State” by Jun Song; Hong-

yi Fan. Journal Reference:Int J. Theor. Phys. 51 229 (2012); Review Number: MR2870433.

t. “Para-Grassmannian Coherent and Squeezed States for Pseudo-Hermitian q-Oscillator

and their Entanglement” by Yusef MALEKI. Journal Reference: SIGMA 7 084 (2011);

Review Number: MR2861192.

u. “Non-Markovian dynamics and entanglement of two-level atoms in a common field”

by C H Fleming; N I Cummings; Charis Anastopoulos; B L Hu. Journal Reference: J. Phys.

A: Math. Theor. 45 065301 (2012); Review Number: MR2881061.

v. “Atomic Coherent States and Sphere Maps” by Robert Gilmore. Journal Reference:

J. Phys. A:Math. Theor. 45 244024 (2012); Review Number: MR2930519.

w. “ Gazeau-Kaluder Cat States” by Jerzy Dajka and Jerzy Luczka. Journal Reference:

J. Phys. A:Math. Theor. 45 244006 (2012); Review Number: MR2930501.

x. “Effective Methods In Investigation Of Irreducible Quantum Operations” by Andrzej

Jamiolkowski. Journal Reference: International J. of Geometric Methods in Mod. Phys. 9

1260014 (2012); Review Number: MR2913152.

2. Invited reviewer for Pramana; J. of Stat. Phys.; J. Phys. A; J. Phys. B; Physica A;

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Quantum Information and Computation (QIC) and Quantum Information and Processing

(QIP); Phys. Rev. A, Phys. Rev. D.

Brief Summary of Research Work:

I have been involved in studies in quantum statistical mechanics. In particular, the major

theme of my work is to show how The theory of Open Quantum Systems provides a

common umbrella to understand quantum optics, quantum information processing, quantum

computing, quantum cryptography, relativistic quantum mechanics, particle physics and

the foundations of quantum mechanics. The theory of open quantum systems addresses

the problems of damping and dephasing in quantum systems by its assertion that all real

systems of interest are in fact ‘open’ systems, each surrounded by its environment. The recent

upsurge of interest in the problem of open quantum systems is because of the spectacular

progress in manipulation of quantum states of matter (atoms, or bosonic or fermionic gases

or molecules), encoding, transmission and processing of quantum information, for all of

which understanding and control of the environmental impact are essential. The Nobel

Prize for 2012 was awarded to D. J. Wineland and S. Haroche for experimental justifications

of quantum coherence and its decay in realistic scenarios. In a number of my works involving

the application of open system ideas to quantum information and quantum optics, I have

made use of the experimental results of Wineland and Haroche.

The projects I have been involved in range from the fundamental aspects of quantum

statistical mechanics to the mathematical physics aspects of canonical transformations in

Fock space. Over the last few years I have been developing a graphical representation

of quantum mechanics. I have also been involved in studies in quantum optics including

the study of quantum nondemolition systems and those directed towards the control over

decoherence in open quantum systems, having relevance to, for example, quantum computers.

I have used open system ideas to quantum random walk which is studied from the point

of view of the interplay between symmetries and noise. I have also been involved in work

related to phases in open quantum systems and have applied open system ideas to quantum

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computation.

A broad theme that I have started work on is the connection between geometry and

statistical mechanics. In a study of complex systems use is made of Renyi and Tsallis

entropies, generalizations of the well known Shannon entropy. The entropic formulation

of statistical mechanics is the ingredient which enables a connection between statistical

mechanics and the corresponding Riemannian geometry. An investigation into the most

general meaning of intrinsic Riemannian geometry for complex systems is made by studying

the Ricci curvature of a number of physical situations modeled by Renyi and Tsallis entropies.

Also, a two-parameter generalization of Renyi and Tsallis entropies, along with a family of

other entropies, are proposed using a generalized difference operation bringing out their

connection to quantum groups.

I am also interested in the field of nonlinear dynamics. In this context, I have been

involved in some works on low dimesional maps such as the logistic map which have been q-

deformed. I have been working towards reaching a coherent understanding of non-Markovian

phenomena. Ideas from non-Markovian physics find a rich breeding ground for investigations

into quantum thermodynamics and also find a number of practical applications.

I have become interested recently in Flavor Physics that explores the deviations of pre-

dictions from the Standard Model. A major thrust in this direction is the probing of the

foundations of physics at the subatomic level. This can yield a number of surprises. Thus,

on one hand, a study of quantum correlations in neutral mesons reveals features not seen

in stable quantum systems and on the other hand, the use of open system ideas on these

systems leads to predictions that suggest a rethinking of the interpretation of important

observables in particle physics and also suggests background effects which could be possible

signatures of quantum gravity.

I give below a brief summary of the work done as well as of the work in progress.

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1 Open quantum systems

• The dynamics of an open quantum system exhibiting quantum Brownian motion is

analyzed when the coupling between the system and its environment is nonlinear, and

the system and the reservoir are initially correlated. For couplings quadratic in the en-

vironment variables, the influence functional for the system is obtained perturbatively

up to second order in the coupling constant, and then the propagator is explicitly evalu-

ated when the particle is under the influence of a harmonic potential and an additional

anharmonic potential, the so-called Washboard potential. As an application of the

propagator, the master equation and the Wigner equation are obtained for the quan-

tum Brownian particle moving in a harmonic potential for the generalized correlated

initial condition, and then for the specific case of the simplified ’thermal’ initial condi-

tion. The system is shown to obey the corresponding fluctuation-dissipation theorem

(ref. [3]).

• The effect of squeezing and modulation on the decoherence and dissipation properties

of an open quantum system are studied. The functional integral formalism is used

to provide a unified treatment of the effect of squeezing of the bath and frequency

modulation of the system bath coupling on the decoherence and dissipation properties

of a quantum open system. The system chosen is a standard one consisting of a particle

in a harmonic oscillator potential interacting with a bath of harmonic oscillators by a

coupling of the position-position kind. Using an ohmic bath and the high temperature

limit the coefficients of the master equation describing dissipation and decoherence are

obtained and analyzed (ref. [4]).

• Use is made of the study (ref. [5]) for some applications of canonical transformations.

It is shown that the single-mode and the n-mode squeezing operators are elements of

the group of canonical transformations. An application is made, in the context of open

quantum systems, by studying the effect of squeezing of the bath on the decoherence

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properties of the system. Two cases are analyzed. In the first case the bath consists

of a massless bosonic field with the bath reference states being the squeezed vacuum

states and squeezed thermal states while in the second case a system consisting of a

harmonic oscillator interacting with a bath of harmonic oscillators is analyzed with the

bath being initially in a squeezed thermal state (ref. [6]).

• A study is made of open quantum systems where the coupling between the system and

its environment is of a quantum nondmolition (QND) type. Such a system undergoes

decoherence without dissipation of energy. The master equation for the evolution of

such a system under the influence of a squeezed thermal bath is obtained. From the

master equation it can be seen explicitly that the process involves decoherence without

any dissipation. The decoherence causing term in the high and zero temperature limits

are obtained and are seen to match with known results in the different temperature

regimes for the case of a thermal bath. A comparison is made between the quantum

statistical properties of QND and non-QND (i.e., involving decoherence as well as

dissipation) types of evolution (ref. [9]).

• The equation for the Wigner function describing the reduced dynamics of a single har-

monic oscillator, coupled to an oscillator bath, was obtained by Karrlein and Grabert

[Phys. Rev. E 55, 153 (1997)]. It was shown that for thermal initial conditions the

equation reduces, in the classical limit, to the corresponding classical Fokker-Planck

equation obtained by Adelman [J. Chem Phys. 64, 124 (1976)]. However for sep-

arable initial conditions the Adelman equations were not recovered. This paradox

involving the classical limit of a single harmonic oscillator, coupled to an oscillator

bath for different initial conditions of the system, both separable as well as thermal

initial conditions, is resolved in this work thereby clarifying the physical relevance of

different initial conditions. It is shown that for separable initial conditions, the classi-

cal Langevin equation obtained from the oscillator bath model is somewhat different

18

from the one considered by Adelman. The corresponding Fokker-Planck equation is

obtained and is shown to exactly match with the classical limit of the equation for the

Wigner function obtained from the master equation for separable initial conditions.

The reason why thermal initial conditions correspond to Adelman’s solution is also

discussed (ref. [10]).

• For a realistic, experimental realization of Quantum Information, it is essential to have

an understanding of Open Quantum Systems. Here an introduction, partly aimed at

students, is provided to some aspects of Open Quantum Systems which are of particular

relevance to Quantum Information. This is followed by some simple applications such

as Geometric Phase, Channel Capacity, Cryptography and a Deleter (ref. [1]).

2 Mathematical Physics

• The general problem of a single two-level atom interacting with a multimode radiation

field (without the rotating-wave approximation) which is additionally coupled to a

thermal reservoir is considered. Using the method of bosonization of the spin operators

in the Hamiltonian, and working in the Bargmann representation for all the boson

operators, the propagator for the composite system is obtained using the techniques

of functional integration, under a reasonable approximation scheme. The propagator

is explicitly evaluated for a simplified version of the system with one spin and coupled

single-mode field. The results are checked on a model describing damped harmonic

oscillator (ref. [2]).

• Canonical transformations on Fock space are studied using the coherent (normalized

exponential) and the ultracoherent vectors. The connection between the Weyl oper-

ator and homogeneous canonical transformations is presented and its action on the

coherent and the ultracoherent vector is given. The group action of the unitary ray

representations of the canonical group, in Fock space, is illustrated by its action on

19

the exponential and the ultracoherent vectors. The action of a generalized quadratic

Hamiltanian, using its differential operator form in the Bargmann-Fock Space, on the

ultracoherent functions is studied (ref. [5]).

• In the scheme of a quantum non-demolition (QND) measurement, an observable is

measured without perturbing its evolution. QND measurement schemes have been

suggested to be able to surpass the standard quantum limit of phase measurements

and reach the Heisenberg limit. In this work such shemes are studied taking the ef-

fect of decoherence into consideration. A study is made of a number of QND ‘Open

System’ Hamiltonians and their propagators are obtained. Two of these propagators

are shown to be connected to the squeezing and rotation operations. Squeezing and

rotation being both phase space area-preserving canonical transformations, this brings

out an interesting connection between the energy-preserving QND Hamiltonians and

homogeneous linear canonical transformations. Using the methods of functional in-

tegration and bosonization the details of these QND propagators and some of their

variants are worked out. The explicit determination of the propagators of these many-

body systems could apart from their technical relevance also shed some light on the

problem of QND measurement schemes (refs. [8,7]).

• In this work a graphical representation of quantum states is proposed. Pure states

require weighted digraphs with complex weights, while mixed states need, in general,

edge weighted digraphs with loops; constructions which, to the best of our knowl-

edge, are new in the theory of graphs. Both the combinatorial as well as the signless

Laplacian are used for graph representation of quantum states. We also provide some

interesting analogies between physical processes and graph representations. Entangle-

ment between two qubits is approached by the development of graph operations that

simulate quantum operations, resulting in the generation of Bell and Werner states. As

a biproduct, the study also leads to separability criteria using graph operations. This

20

paves the way for a study of genuine multipartite correlations using graph operations

(ref. [39]).

• We implement a graph theoretical realization of local unitary transformations, imple-

mented by single qubit Pauli gates, by adapting techniques of graph switching. This

leads to the concept of local unitary equivalent graphs. We illustrate our method by a

few, well known, local unitary transformations implemented by single qubit Pauli and

Hadamard gates. The work is then extended to provide a graphi- cal implementation

of CNOT gates. The well known two-qubit entangled states, Bell states, are shown

to emerge from our constructions. We thus have a graphical realization of universal

quantum computation (ref. [49]).

• We consider the separability problem for bipartite quantum states arising from graphs.

Earlier it was proved that the degree criterion is the graph theoretical counterpart of

the familiar PPT criterion for separability, although there are entangled states with

positive partial transpose for which degree criterion fails. Here, we introduce the

concept of partially symmetric graphs and degree symmetric graphs by using the well-

known concept of partial transposition of a graph and degree criteria, respectively.

Thus, we provide classes of bipartite separable states of dimension m× n arising from

partially symmetric graphs. We identify partially asymmetric graphs which lack the

property of partial symmetry. Finally we develop a combinatorial procedure to create

a partially asymmetric graph from a given partially symmetric graph. We show that

this combinatorial operation can act as an entanglement generator for mixed states

arising from partially symmetric graphs (ref. [63]).

• Construction of graphs with equal eigenvalues (co-spectral graphs) is an interesting

problem in spectral graph theory. Seidel switching is a well-known method for gener-

ating co-spectral graphs. From a matrix theoretic point of view, Seidel switching is a

combined action of a number of unitary operations on graphs. Recently, it has been

21

shown that significant connections between graph and quantum information theories.

Corresponding to Laplacian matrices of any graph there are quantum states useful in

quantum computing. From this point of view, graph theoretical problems are mean-

ingful in the context of quantum information. This work describes Seidel switching

from a quantum perspective. Here, we generalize Seidel switching to weighted directed

graphs. We use it to construct graphs with equal Laplacian and signless Laplacian

spectra and consider density matrices corresponding to them. Hence Seidel switching

is a technique to generate cospectral density matrices. Next, we show that all the uni-

tary operators used in Seidel switching are global unitary operators. Global unitary

operators can be used to generate entanglement, a benchmark phenomena in quantum

information processing (ref. [67]).

• Quantum discord refers to an important aspect of quantum correlations for bipartite

quantum systems. In our earlier works we have shown that corresponding to every

graph (combinatorial) there are quantum states whose properties are reflected in the

structure of the corresponding graph. Here, we attempt to develop a graph theoretic

study of quantum discord that corresponds to a necessary and sufficient condition of

zero quantum discord states which says that the blocks of density matrix correspond-

ing to a zero quantum discord state are normal and commute with each other. These

blocks have a one to one correspondence with some specific subgraphs of the graph

which represents the quantum state. We obtain a number of graph theoretic properties

representing normality and commutativity of a set of matrices which are indeed arising

from the given graph. Utilizing these properties we define graph theoretic measures

for normality and commutativity that results a formulation of graph theoretic quan-

tum discord. We identify classes of quantum states with zero discord using the said

formulation (ref. [68]).

• In this paper we determine the class of quantum states whose density matrix representa-

22

tion can be derived from graph Laplacian matrices associated with a weighted directed

graph and we call them graph Laplacian quantum states. Then we obtain structural

properties of these graphs such that the corresponding graph Laplacian states have

zero quantum discord by investigating structural properties of clustered graphs which

provide a family of commuting normal matrices formed by the blocks of its Laplacian

matrices. We apply these results on some important mixed quantum states, such as

the Werner, Isotropic, and X-states (ref. [69]).

3 Dynamics of entanglement and Quantum Correla-

tions in open quantum systems

• We analyze the dynamics of entanglement in a two-qubit system interacting with an

initially squeezed thermal environment via a quantum nondemolition system-reservoir

interaction, with the system and reservoir assumed to be initially separable. We com-

pare and contrast the decoherence of the two-qubit system in the case where the qubits

are mutually close-by (‘collective regime’) or distant (‘localized regime’) with respect to

the spatial variation of the environment. Sudden death of entanglement (as measured

by concurrence) is shown to occur in the localized case rather than in the collective

case, where entanglement tends to ‘ring down’. Using a novel quantification of mixed

state entanglement, we show that there are noise regimes where even though entangle-

ment (as measured by concurrence) vanishes, the state is still available for applications

like NMR quantum computation, because of the presence of a pseudo-pure component.

The dynamics is found to satisfy a spin-flip symmetry operation. We give an effective

temperature dependent dynamics for the collective decoherence regime and make an

application of the two-qubit dynamics to quantum communication, by using it on a

simplified model of quantum repeaters (ref. [21]).

• We study the dynamics of entanglement in a two-qubit system interacting with a

squeezed thermal bath via a dissipative system-reservoir interaction with the system

23

and reservoir assumed to be in a separable initial state. The resulting entanglement is

studied by making use of a recently introduced measure of mixed state entanglement

via a probability density function which gives a statistical and geometrical characteri-

zation of entanglement by exploring the entanglement content in the various subspaces

spanning the two-qubit Hilbert space. We also make an application of the two-qubit

dissipative dynamics to a simplified model of quantum repeaters (ref. [22]).

• The effect of a number of mechanisms designed to suppress decoherence in open quan-

tum systems are studied with respect to their effectiveness at slowing down the loss

of entanglement. The effect of photonic band-gap materials and frequency modulation

of the system-bath coupling are along expected lines in this regard. However, other

control schemes, like resonance fluorescence, achieve quite the contrary: increasing

the strength of the control kills entanglement off faster. The effect of dynamic de-

coupling schemes on two qualitatively different system-bath interactions are studied

in depth. Dynamic decoupling control has the expected effect of slowing down the

decay of entanglement in a two-qubit system coupled to a harmonic oscillator bath

under non-demolition interaction. However, non-trivial phenomena are observed when

a Josephson charge qubit, strongly coupled to a random telegraph noise bath, is sub-

ject to decoupling pulses. The most striking of these reflects the resonance fluorescence

scenario in that an increase in the pulse strength decreases decoherence but also speeds

up the sudden death of entanglement. This demonstrates that the behaviour of deco-

herence and entanglement in time can be qualitatively different in the stong-coupling

non-Markovian regime (ref.[31]).

• In this work, we study quantum correlations in mixed states. The states studied

are modeled by a two-qubit system interacting with its environment via a quantum

non demolition (purely dephasing) as well as dissipative type of interaction. The

entanglement dynamics of this two qubit system is analyzed. We make a comparative

24

study of various measures of quantum correlations, like Concurrence, Bell’s inequality,

Discord and Teleportation fidelity, on these states, generated by the above evolutions.

We classify these evoluted states on basis of various dynamical parameters like bath

squeezing parameter r, inter-qubit spacing r12, temperature T and time of system-

bath evolution t. In this study, in addition we report the existence of entangled states

which do not violate Bell’s inequality, but can still be useful as a potential resource

for teleportation. Moreover we study the dynamics of quantum as well as classical

correlation in presence of dissipative coherence (ref.[26]).

• The classicalization of a decoherent discrete-time quantum walk on a line or an n-cycle

can be demonstrated in various ways that do not necessarily provide a geometry-

independent description. For example, the position probability distribution becomes

increasingly Gaussian, with a concomitant fall in the standard deviation, in the former

case, but not in the latter. As another example, each step of the quantum walk on a

line may be subjected to an arbitrary phase gate, without affecting the position prob-

ability distribution, no matter whether the walk is noiseless or noisy. This symmetry,

which is absent in the case of noiseless cyclic walk, but is restored in the presence of

sufficient noise, serves as an indicator of classicalization, but only in the cyclic case.

Here we show that the degree of quantum correlations between the coin and position

degrees of freedom, quantified by a measure based on the disturbance induced by local

measurements [Luo, Phys. Rev. A 77, 022301 (2008)], provides a suitable measure of

classicalization across both type of walks. Applying this measure to compare the two

walks, we find that cyclic quantum walks tend to classicalize faster than quantum walks

on a line because of more efficient phase randomization due to the self-interference of

the two counter-rotating waves. We model noise as acting on the coin, and given by

the squeezed generalized amplitude damping (SGAD) channel, which generalizes the

generalized amplitude damping channel (ref.[27]).

25

• We present a novel scheme for generating entanglement between two spatially sepa-

rated systems. The scheme makes use of the spatial entanglement generated by the

interference effect during the evolution of a single-particle quantum walk. Any two

systems which can interact with the spatial modes entangled during the walk evolu-

tion can be entangled using this scheme. A notable feature is the ability to control the

quantum walk dynamics and its localization in position space resulting in a substan-

tial control and improvement in the entanglement output. Different implementation

schemes to entangle spatially separated atoms using quantum walk on a photon or a

single atom are presented (ref.[28]).

• Noisy quantum walks are studied from the perspective of comparing their quantumness

as defined by two popular measures, measurement-induced disturbance (MID) and

quantum discord (QD). While the former has an operational definition, unlike the

latter, it also tends to overestimate non-classicality because of lack of optimization over

local measurements. Applied to quantum walks, we find that MID, while acting as a

loose upper bound on QD, still tends to reflect well trends in the behavior of the latter.

However, there are regimes where its behavior is not indicative of non-classicality: in

particular, we find an instance where MID increases with the application of noise,

where we expect a reduction of quantumness (ref.[30]).

• Quantum discord is a prominent measure of quantum correlations, playing an impor-

tant role in expanding its horizon beyond entanglement. Here we provide an oper-

ational meaning of (geometric) discord, which quantifies the amount of non-classical

correlation of an arbitrary quantum system based on its minimal distance from the set

of classical states, in terms of teleportation fidelity for general two qubit and d⊗ d di-

mensional isotropic and Werner states. A critical value of the discord is found beyond

which the two qubit state must violate the Bell inequality. This is illustrated by an

open system model of a dissipative two qubit. For the d ⊗ d dimensional states the

26

lower bound of discord is shown to be obtainable from an experimentally measurable

witness operator (ref. [41]).

• Bipartite entangled states in arbitrary dimensions are studied and different bounds for

the teleportation fidelity are obtained. In addition, various relations between telepor-

tation fidelity and the entanglement measures depending upon Schmidt rank of the

states are established. These relations and bounds help in to determine the amount

of entanglement required for teleportation. This amount of entanglement required for

teleportation is called “Entanglement of Teleportation”. These bounds are used to de-

termine the teleportation fidelity as well as the entanglement required for teleportation

of states modeled by a two qutrit mixed system as well as two qubit open quantum

systems (ref. [42]).

• A master equation is constructed for a global system-bath interaction both in the

absence as well as presence of non-Markovian noise. The master equation is exactly

solved for a special class of two qubitX states (which contains Bell diagonal and Werner

states). The l1 norm of coherence is calculated and the dynamics of quantum coherence

in the presence of a global system-bath interaction is observed. It is shown that the

global part of the system-bath interaction compensates for the decoherence, resulting

in the slow down of coherence decay. The concurrence and the Fisher information,

explicitly calculated for a particular two qubit Werner state, indicate that the decay of

these quantum features also slow down under a global system-bath interaction. Also

shown is the feature that the coherence is the most robust of all the three non-classical

features under environmental interaction. Entanglement is seen to be the most costly

of them all. For an appropriately defined limiting case, all the three quantities show

freezing behaviour. This limiting condition is attainable when the separations between

the energy levels of both the atomic qubits are small (ref. [62]).

27

4 Phase distributions in open quantum systems

• The dynamics of quantum phase distribution associated with the reduced density ma-

trix of a system, as the system evolves under the influence of its environment with

a quantum nondemolition type of coupling is quantitatively analyzed. The system

is taken to be either an oscillator (harmonic or anharmonic) or a two-level atom (or

equivalently, a spin-1/2 system), and the environment modelled as a bath of harmonic

oscillators, initially in a general squeezed thermal state. The impact of the different en-

vironmental parameters is explicitly brought out on the dynamics of the quantum phase

distribution of the system starting at various initial states. The results are applicable

to a variety of physical systems now studied experimentally with QND measurements

(ref. [11]).

• The previous work is extended to study the phase distribution in QND as well as

dissipative systems. The impact of the different environmental parameters on the

dynamics of the quantum phase distribution for the system starting out in various

initial states, is explicitly brought out. An interesting feature that emerges from the

work is that the relationship between squeezing and temperature effects depends on

the type of system-bath interaction. In the case of quantum nondemolition type of

interaction, squeezing and temperature work in tandem, producing a diffusive effect on

the phase distribution. In contrast, in case of a dissipative interaction, the influence

of temperature can be counteracted by squeezing, which manifests as a resistence to

randomization of phase. The phase distributions are used to bring out a notion of

complementarity in atomic systems. A study is made of the dispersion of the phase

using the phase distributions conditioned on particular initial states of the system.

This would be of direct relevance to a number of experiments (ref. [14]).

28

5 Open quantum systems and quantum computation

• Geometric phase is intrinsically related to the kinematics of the path followed by the

system in its Hilbert space. Both from the point of view theoretical interest as well

as practical implications, as for example with respect to quantum computers, it is

interesting to study geometric phase in the context of open quantum systems. In

this work we make such a study for a number of open system models with the bath

(reservoir) being modelled as a squeezed thermal bath, with the system-bath interaction

being taken to be both non-dissipative (QND) as well as dissipative. An interesting

feature coming out of this work is the contrasting interplay between squeezing and

thermal effects in the two types of system-bath interactions. Whereas for the QND

case, squeezing plays a role similar to temperature in suppressing the geometric phase,

in the dissipative case squeezing is seen to oppose thermal effects in some regimes.

This could have practical implications in the design of realistic geometric phase gates

for quantum computation (ref. [12]).

• The work done on the reduced dynamics of the multi-qubit system in (ref. [21], [22]) is

used to compute the geometric phase of a two-qubit system interacting with its bath

via both QND as well as dissipative interactions (ref. [23]).

• Environment-induced decoherence presents a great challenge to realizing a quantum

computer. In this work is brought out the somewhat surprising fact that decoherence

can be useful, indeed necessary, for practical quantum computation, in particular, for

effective erasure of quantum memory by way of preparing the initial state of the quan-

tum computer. The environment must in general be dissipative. A specific example

is the amplitude damping channel provided by a two-level system interacting with its

environment in the weak Born-Markov rotating wave approximation (ref. [13]).

• Geometric phase plays an important role in evolution of pure or mixed quantum states.

However, when a system undergoes decoherence the development of geometric phase

29

may be inhibited. Here, we show that when a quantum system interacts with two

competing environments there can be enhancement of geometric phase. This effect

is akin to Parrondo like effect on the geometric phase which results from quantum

frustration of decoherence. Our result suggests that the mechanism of two competing

decoherence can be useful in fault tolerant holonomic quantum computation (ref. [43]).

6 Quantum communication

• A new noisy quantum channel called “The squeezed generalized amplitude damping

channel” is introduced, which depicts the physics of dissipative interaction with a

squeezed thermal bath, governed by a Lindblad-type evolution. The action of this

channel is given in terms of Kraus operators. As expected, this channel reduces to the

“generalized amplitude damping channel” when the squeezing parameters are set to

zero. This work brings out the physics behind this new channel, its implications and

properties. As an application of this channel to quantum communication, its classical

capacity is studied (ref. [20]).

• The principle of a cryptographic switch is illustrated using a quantum system, in which

a third party (Charlie) can control to a continuously varying degree the amount of in-

formation the receiver (Bob) receives, after the sender (Alice) has sent her information.

Suppose Charlie transmits a Bell state to Alice and Bob. Alice uses dense coding to

transmit two bits to Bob. Only if the 2-bit information corresponding to choice of Bell

state is made available by Charlie to Bob can the latter recover Alice’s information.

By varying the information he gives, Charlie can continuously vary the information

recovered by Bob. The performance of the protocol subjected to the squeezed general-

ized amplitude damping channel is considered. A number of practical situations where

a cryptographic switch would be of use are presented (ref. [35]).

• We shown that a realistic, controlled bidirectional remote state preparation is possible

30

using a large class of entangled quantum states having a particular structure. Existing

protocols of probabilistic, deterministic and joint remote state preparation are gener-

alized to obtain the corresponding protocols of controlled bidirectional remote state

preparation (CBRSP). A general way of incorporating the effects of two well known

noise processes, the amplitude-damping and phase-damping noise, on the probabilistic

CBRSP process is studied in detail by considering that noise only affects the travel

qubits of the quantum channel used for the probabilistic CBRSP process. Also indi-

cated is how to account for the effect of these noise channels on deterministic and joint

remote state CBRSP protocols (ref. [50]).

• The effect of noise on various protocols of secure quantum communication has been

studied. Specifically, we have investigated the effect of amplitude damping, phase

damping, squeezed generalized amplitude damping, Pauli type as well as various col-

lective noise models on the protocols of quantum key distribution, quantum key agree-

ment,quantum secure direct quantum communication and quantum dialogue. From

each type of protocol of secure quantum communication, we have chosen two protocols

for our comparative study; one based on single qubit states and the other one on entan-

gled states. The comparative study reported here has revealed that single-qubit-based

chemes are generally found to perform better in the presence of amplitude damping,

phase damping, squeezed generalized amplitude damping noises, while entanglement-

based protocols turn out to be preferable in the presence of collective noises. It is

also observed that the effect of noise entirely depends upon the number of rounds of

quantum communication involved in a scheme of quantum communication. Further,

it is observed that squeezing, a completely quantum mechanical resource present in

the squeezed generalized amplitude channel, can be used in a beneficial way as it may

yield higher fidelity compared to the corresponding zero squeezing case (ref. [64]).

• A set of schemes for secure quantum communication are analyzed under the influence

31

of non-Markovian channels. By comparing with the corresponding Markovian cases, it

is seen that the average fidelity in all these schemes can be maintained for relatively

longer periods of time. Effects of non-Markovinan noise on a number of facets of quan-

tum cryptography, such as quantum secure direct communication, deterministic secure

quantum communication and their controlled counterparts, such as quantum dialogue,

quantum key distribution, quantum key agreement have been extensively investigated.

Specifically, a scheme for controlled quantum dialogue (CQD) is analyzed over damp-

ing, dephasing and depolarizing non-Markovian channels, and subsequently, the effect

of these non-Markovian channels on the other schemes of ecure quantum communi-

cation is deduced from the results obtained for CQD. The damped non-Markovian

channel causes, a periodic revival in the fidelity; while fidelity is observed to be sus-

tained under the influence of the dephasing non-Markovian channel. The depolarizing

channel, as well as the other non-Markovian channels discussed here, show that the ob-

tained average fidelity subjected to noisy environment depend on the coupling strength

and the number of rounds of quantum communication involved in a particular scheme

(ref. [66]).

• Quantum Key Distribution (QKD) is a key exchange protocol which is implemented

over free space optical links and optical fiber cable. When direct communication is

not possible, QKD is performed over fiber cables, but the imperfections in detectors

used at receiver side and also the material properties of fiber cables limit the long

distance communication. Free space based quan- tum key distribution is free from

such limitations, and can pave way for satellite based quantum communication to set

up a global network for sharing secret messages. To implement free space optical (FSO)

links, it is essential to study the effect of atmospheric turbulence. Here, an analysis is

made for satellite based quantum communication using QKD protocols. The results

obtained indicate that SARG04 protocol is an effective approach for satellite based

quantum communication (ref. [77]).

32

• In quantum key distribution, one conservatively assumes that the eavesdropper Eve is

restricted only by physical laws, whereas the legitimate parties, namely the sender Alice

and receiver Bob, are subject to realistic constraints, such as noise due to environment-

induced decoherence. In practice, Eve too may be bound by the limits imposed by

noise, which can give rise to the possibility that decoherence works to the advantage of

the legitimate parties. A particular scenario of this type is one where Eve can’t replace

the noisy communication channel with an ideal one, but her eavesdropping channel

itself remains noiseless. Here, we point out such a situation, where the security of the

Ping-Pong protocol (modified to a key distribution scheme) against a noise-restricted

adversary improves under a non-unital noisy channel, but deteriorates under unital

channels (ref. [78]).

7 Quantum information

• A study is made of some discrete symmetries of unbiased (Hadamard) and biased

quantum walks on a line, which are shown to hold even when the quantum walker is

subjected to environmental effects. The noise models considered in order to account

for these effects are the phase flip, bit flip and generalized amplitude damping chan-

nels. The numerical solutions are obtained by evolving the density matrix, but the

persistence of the symmetries in the presence of noise is proved using the quantum

trajectories approach. These investigations can be relevant to the implementation of

quantum walks in various known physical systems. Implementation of these ideas in

the case of NMR quantum information processor and ultra cold atoms is discussed (ref.

[18]).

• Augmenting the unitary transformation which generates a quantum walk by a general-

ized phase gate G is a symmetry for both noisy and noiseless quantum walk on a line,

in the sense that it leaves the position probability distribution invariant. However,

this symmetry breaks down in the case of a quantum walk on an n-cycle, and hence

33

can be regarded as a probe of the walk topology. Noise, modelled here as phase flip

and generalized amplitude damping channels, tends to restore the symmetry because

it classicalizes the walk. However, symmetry restoration happens even in the regime

where the walker is not entirely classical, because noise also has the effect of desensi-

tizing the operation G to the walk topology. This provides a nontrivial instance of the

interplay between geometry and noise in a quantum information processing system. We

discuss methods for physical implementation, and talk about the wider implications to

condensed matter systems (ref. [19]).

• Quantum walk models have been used as an algorithmic tool for quantum computation

and to describe various physical processes. This paper revisits the relationship between

relativistic quantum mechanics and the quantum walks. We show the similarities of

the mathematical structure of the decoupled and coupled form of the discrete-time

quantum walk to that of the Klein-Gordon and Dirac equations, respectively. In the

latter case, the coin emerges as an analog of the spinor degree of freedom. Discrete-

time quantum walk as a coupled form of the continuous-time quantum walk is also

shown by transforming the decoupled form of the discrete-time quantum walk to the

Schrodinger form. By showing the coin to be a means to make the walk reversible, and

that the Dirac-like structure is a consequence of the coin use, our work suggests that

the relativistic causal structure is a consequence of conservation of information. How-

ever, decoherence (modelled by projective measurements on position space) generates

entropy that increases with time, making the walk irreversible and thereby producing

an arrow of time. Lieb-Robinson bound is used to highlight the causal structure of the

quantum walk to put in perspective the relativistic structure of quantum walk, maxi-

mum speed of the walk propagation and the earlier findings related to the finite spread

of the walk probability distribution. We also present a two-dimensional quantum walk

model on a two state system to which the study can be extended (ref.[24]).

34

• Single-qubit channels are studied under two broad classes: amplitude damping channels

and generalized depolarizing channels. A canonical derivation of the Kraus represen-

tation of the former, via the Choi isomorphism is presented for the general case of a

system’s interaction with a squeezed thermal bath. This isomorphism is also used to

characterize the difference in the geometry and rank of these channel classes. Under

the isomorphism, the degree of decoherence is quantified according to the mixedness

or separability of the Choi matrix. Whereas the latter channels form a 3-simplex, the

former channels do not form a convex set as seen from an ab initio perspective. Fur-

ther, where the rank of generalized depolarizing channels can be any positive integer

upto 4, that of amplitude damping ones is either 2 or 4. Various channel performance

parameters are used to bring out the different influences of temperature and squeezing

in dissipative channels. In particular, a noise range is identified where the distin-

guishability of states improves inspite of increasing decoherence due to environmental

squeezing. (ref. [40])

• On account of the Abel-Galois no-go theorem for the algebraic solution to quintic and

higher order polynomials, the eigenvalue problem and the associated characteristic

equation for a general noise dynamics in dimension d via the Choi-Jamiolkowski ap-

proach cannot be solved in general via radicals. A way around this impasse is provided

by decomposing the Choi matrix into simpler, not necessarily positive, Hermitian oper-

ators that are diagonalizable via radicals, which yield a set of ‘positive’ and ‘negative’

Kraus operators. The price to pay is that the sufficient number of Kraus operators is d4

instead of d2, sufficient in the Kraus representation. We consider various applications

of the formalism: the Kraus repesentation of the 2-qubit amplitude damping channel,

the noise resulting from a 2-qubit system interacting dissipatively with a vacuum bath;

defining the maximally dephasing and purely dephasing components of the channel

in the new representation, and studying their entanglement breaking and broadcast

properties (ref. [44]).

35

• Quantum Algorithms have long captured the imagination of computer scientists and

physicists primarily because of the speed up achieved by them over their classical

counterparts using principles of quantum mechanics. Entanglement is believed to be

the primary phenomena behind this speed up. However their precise role in quantum

algorithms is yet unclear. In this article, we explore the nature of entanglement in

the Grovers search algorithm. This algorithm enables searching of elements from an

unstructured database quadratically faster than the best known classical algorithm.

Geometric measure of entanglement has been used to quantify and analyse entangle-

ment across iterations of the algorithm. We reveal how the entanglement varies with

increase in the number of qubits and also with the number of marked or solution states.

Numerically, it is seen that the behaviour of the maximum value of entanglement is

monotonous with the number of qubits. Also, for a given value of the number of

qubits, a change in the marked states alters the amount of entanglement. The amount

of entanglement in the final state of the algorithm has been shown to depend solely

on the nature of the marked states. Explicit analytical expressions are given showing

the variation of entanglement with the number of iterations and the global maximum

value of entanglement attained across all iterations of the algorithm (ref. [46]).

8 Error Correction

• Characterizing noisy quantum processes is important to quantum computation and

communication (QCC), since quantum systems are generally open. To date, all meth-

ods of characterization of quantum dynamics (CQD), typically implemented by quan-

tum process tomography, are off-line, i.e., QCC and CQD are not concurrent, as they

require distinct state preparations. Here we introduce a method, quantum error cor-

rection based characterization of dynamics (QECCD), in which the initial state is any

element from the code space of a quantum error correcting code that can protect the

state from arbitrary errors acting on the subsystem subjected to the unknown dynam-

36

ics. The statistics of stabilizer measurements, with possible unitary pre-processing

operations, are used to characterize the noise, while the observed syndrome can be

used to correct the noisy state. Our method requires at most 2(4n1) configurations to

characterize arbitrary noise acting on n qubits (ref. [48]).

• A quantum error correcting code is a subspace C such that allowed errors acting on

any state in C can be corrected. A quantum code for which state recovery is only

required up to a logical rotation within C, can be used for detection of errors, but not

for quantum error correction. Such a code with stabilizer structure, which we call an

ambiguous stabilizer code (ASC), can nevertheless be useful for the characterization

of quantum dynamics (CQD). The use of ASCs can help lower the size of CQD probe

states used, but at the cost of increased number of operations (ref. [47]).

• The method of quantum error correction based characterization of quantum dynamics

(QECCD) is applied to developing a protocol for performing quantum process tomog-

raphy on a two-qubit system interacting dissipatively with a vacuum bath. The method

uses a 5-qubit quan- tum error correcting code that corrects arbitrary errors on the

first two qubits, and thus saturates the quantum Hamming bound. The noise model

considered allows for both correlated and independent noise on the two-qubit system.

Identifying the degree of correlation of the noise with the departure of the correspond-

ing process matrix from the product form, we study its dependence on the time of

evolution and inter-qubit separation. We find that the noise correlation (maximized

over time) falls monotonically with inter-qubit separation. Time evolution of the noise

correlation shows different behavior for collective vs independent noise: in both cases,

it attains a limiting value, but shows initial oscillatory behavior in the former case (ref.

[61]).

37

9 Open quantum sytems & Foundations of quantum

mechanics

• Quantum theory of Stern-Gerlach System in contact with a lineraly dissipative environ-

ment at an arbitrary temperature is studied. Here use is made of the Feynman-Vernon

influence functional technique generalized to incorporate non-separable initial condi-

tions. The behaviour of the density matrix in the long-time limit is analyzed and the

time scale of decay of the elements off-diagonal in the coordinate and momentum space

are computed for the entire temperature range (ref. [1]).

• An information theoretic interpretation of the number-phase complementarity in atomic

systems is developed, where phase is treated as a continuous positive operator valued

measure (POVM). The relevant uncertainty principle is obtained as an upper bound

on a sum of knowledge of these two observables for the case of two-level systems. A

tighter bound characterizing the uncertainty relation is obtained numerically in terms

of a weighted knowledge sum involving these variables. We point out that complemen-

tarity in these systems departs from mutual unbiasededness in two signalificant ways:

first, the maximum knowledge of a POVM variable is less than log(dimension) bits;

second, surprisingly, for higher dimensional systems, the unbiasedness may not be mu-

tual but unidirectional in that phase remains unbiased with respect to number states,

but not vice versa. Finally, we study the effect of non-dissipative and dissipative noise

on these complementary variables for a single-qubit system (ref. [15]).

• A unified, information theoretic interpretation of the number-phase complementarity

that is applicable both to finite-dimensional (atomic) and infinite-dimensional (oscil-

lator) systems is developed, with number treated as a discrete Hermitian observable

and phase as a continuous positive operator valued measure (POVM). The relevant

uncertainty principle is obtained as a lower bound on entropy excess, X, the difference

between the entropy of one variable, typically the number, and the knowledge of its

38

complementary variable, typically the phase, where knowledge of a variable is defined

as its relative entropy with respect to the uniform distribution. In the case of finite

dimensional systems, a weighting of phase knowledge by a factor µ (> 1) is necessary

in order to make the bound tight, essentially on account of the POVM nature of phase

as defined here. Numerical and analytical evidence suggests that µ tends to 1 as sys-

tem dimension becomes infinite. We study the effect of non-dissipative and dissipative

noise on these complementary variables for oscillator as well as atomic systems (ref.

[16], [17]).

10 Non-Markovian Physics

• In the case of the discrete time coined quantum walk the reduced dynamics of the

coin shows non-Markovian recurrence features due to information back-flow from the

position degree of freedom. Here we study how this non-Markovian behavior is modified

in the presence of open system dynamics. In the process, we obtain useful insights into

the nature of non-Markovian physics. In particular, we show that in the case of (non-

Markovian) random telegraph noise (RTN), a further discernible recurrence feature is

present in the dynamics. Moreover, this feature is correlated with the localization of

the walker. On the other hand, no additional recurruence feature appears for other

non-Markovian types of noise (Ornstein-Uhlenbeck and Power Law noise). We propose

a power spectral method for comparing the relative strengths of the non-Markovian

component due to the external noise and that due to the internal position degree of

freedom (ref. [73]).

• Quantum non-Markovianity of a quantum noisy channel manifests typically as informa-

tion backflow, characterized by the departure of the intermediate map from complete

positivity, though we indicate certain noisy channels that don’t exhibit this behavior.

In complex systems, non-Markovianity becomes more involved on account of subsystem

dynamics. Here we study various facets of non-Markovian evolution, in the context of

39

coined quantum walks, with particular stress on disambiguating the internal vs. envi-

ronmental contributions to non-Markovian backflow. For the above problem of disam-

biguation, we present a general power-spectral technique based on a distinguishability

measure such as trace-distance or correlation measure such as mutual information. We

also study various facets of quantum correlations in the transition from quantum to

classical random walks, under the considered non-Markovian noise models. The poten-

tial for the application of this analysis to the quantum statistical dynamics of complex

systems is indicated (ref. [74]).

• Non-Markovian quantum effects are typically observed in systems interacting with

structured reservoirs. Discrete-time quantum walks are prime example of such sys-

tems in which, quantum memory arises due to the controlled interaction between the

coin and position degrees of freedom. Here we show that the information backflow

that quantifies memory effects can be enhanced when the particle is subjected to un-

correlated static or dynamic disorder. The presence of disorder in the system leads

to localization effects in 1-dimensional quantum walks. We shown that it is possible

to infer about the nature of localization in position space by monitoring the infor-

mation backflow in the reduced system. Further, we study other useful properties of

the reduced system such as entanglement, interference and its connection to quantum

non-Markovianity (ref. [76]).

• We introduce a method to construct non-Markovian variants of completely positive

(CP) dynamical maps, particularly, qubit Pauli channels. We identify non-Markovianity

with the breakdown in CP-divisibility of the map, i.e., appearance of a not-completely-

positive (NCP) intermediate map. In particular, we consider the case of non-Markovian

dephasing in detail. The eigenvalues of the Choi matrix of the intermediate map

crossover at a point which corresponds to a singularity in the canonical decoherence

rate of the corresponding master equation, and thus to a momentary non-invertibility

40

of the map. Thereater, the rate becomes negative, indicating non-Markovianity. We

quantify the non-Markovianity by two methods, one based on CP-divisibility (Hall et

al., PRA 89, 042120, 2014), which doesn’t require optimization but requires normaliza-

tion to handle the singularity, and another method, based on distinguishability (Breuer

et al. PRL 103, 210401, 2009), which requires optimization but is insensitive to the

singularity (ref. [80]).

• We study the violations of Leggett-Garg (LG) inequality in a qubit subjected to

non-Markovian noisy channels such as Random Telegraph Noise (RTN) and Ornstein-

Uhlenbeck Noise (OUN). Quite generally, the state-independence of the violation in

the noiseless case is preserved under the application of noise. Within a given family of

noisy channels (in specific, RTN or OUN), we find an enhancement in the violation in

the non-Markovian case as compared to the Markovian case. We thus find that non-

Markovianity provides a stronger demonstration of quantumness of the system (ref.

[81]).

11 Quantum Thermodynamics

• We show that non-Markovian effects of the reservoirs can be used as a resource to

extract work from an Otto cycle. The state transformation under non-Markovian dy-

namics is cast into a two-step process involving an isothermal process using a Marko-

vian reservoir followed by an adiabatic process. From second law of thermodynamics,

we show that the maximum amount of extractable work from the state prepared un-

der the non-Markovian dynamics quantifies the lower bound of non-Markovianity. We

illustrate our ideas with an explicit example of non-Markovian evolution (ref. [75]).

12 Relativistic Quantum Information

• We make use of the tools of quantum information theory to shed light on the Unruh

effect. Here we study various facets of quantum correlations, such as, Bell inequality

41

violations, entanglement, teleportation and measurement induced decoherence under

the effect of the Unruh channel. The Unruh channel for a mode of a free Dirac field,

as seen by a relativistically accelerated observer, is seen to be noisy and is character-

ized, in this work, by providing its operator-sum representation. A modal qubit thus

appears as if subjected to quantum noise that degrades quantum information, as ob-

served in the accelerated reference frame. We compare and contrast this noise, which

arises from the Unruh effect, from a conventional noise due to environmental decoher-

ence. We show that the Unruh effect produces an amplitude-damping-like channel,

associated with zero temperature, even though the Unruh effect is associated with a

non-zero temperature. Asymptotically, the Bloch sphere subjected to the channel does

not converge to a point, as would be expected by fluctuation-dissipation arguments,

but contracts by a finite factor. We construct for the Unruh effect the inverse chan-

nel, a non-completely-positive map, that reverses the effect, and offer some physical

interpretation (ref. [53]).

• A Bloch vector representation of Unruh channel for a Dirac field mode is developed.

This is used to provide a unified, analytical treatment of quantum Fisher and Skew

information for a qubit subjected to the Unruh channel, both in its pure form as well

as in the presence of experimentally relevant external noise channels. The time evo-

lution of Fisher and Skew information is studied along with the impact of external

environment parameters such as temperature and squeezing. The external noises are

modelled by both purely dephasing phase damping as well as the squeezed generalized

amplitude damping channels. An interesting interplay between the external reservoir

temperature and squeezing on the Fisher and Skew information is observed, in par-

ticular, for the action of the squeezed generalized amplitude damping channel. It is

seen that for some regimes, squeezing can enhance the quantum information against

the deteriorating influence of the ambient environment. Similar features are also ob-

served for the analogous study of Skew information, highlighting the similar origin of

42

the Fisher and Skew information (ref. [60]).

• We show through the Choi matrix approach that the effect of Unruh acceleration on

a qubit is similar to the interaction of the qubit with a vacuum bath, despite the

finiteness of the Unruh temperature. Thus, rather counterintuitvely, from the perspec-

tive of decoherence in this framework, the particle experiences a vacuum bath with a

temperature-modified interaction strength, rather than a thermal bath. We investigate

how this ”relativistic decoherence” is modified by the presence of environmentally in-

duced decoherence, by studying the degradation of quantum information, as quantified

by parameters such as nonlocality, teleportation fidelity, entanglement, coherence and

quantum measurement-induced disturbance (a discord-like measure). Also studied are

the performance parameters such as gate and channel fidelity. We highlight the dis-

tinction between dephasing and dissipative environmental interactions, by considering

the actions of quantum non-demolition and squeezed generalized amplitude damping

channels, respectively, where, in particular, squeezing is shown to be a useful quantum

resource (ref. [65]).

13 Particle Physics and Foundations of Quantum Me-

chanics

• We study the impact of decoherence on B meson systems with specific emphasis on Bs

. For consistency we also study the Bd mesons based on the most recent data. We find

that the Bd mesons are 34 away from total decoherence, while the Bs mesons are seen

to be upto 31 away from total decoherence. Thus, our results prove, with experimental

verity, that neutral meson systems are free from decoherence effects. Therefore, this

provides a very useful laboratory for testing the foundations of quantum mechanics

(ref. [45]).

• The interplay between the various measures of quantum correlations are well known

43

in stable optical and electronic systems. Here we study such foundational issues in

unstable quantum systems. Specifically we study meson-antimeson systems (KK,

BdBd and BsBs), which are produced copiously in meson factories. In particular,

the nonclassicality of quantum correlations which can be characterized in terms of

nonlocality (which is the strongest condition), entanglement, teleportation fidelity or

weaker nonclassicality measures like quantum discord are analyzed. We also study the

impact of decoherence on these measures of quantum correlations, using the semigroup

formalism. A comparison of these measures brings out the fact that the relations

between them can be nontrivially different from those of their stable counterparts such

as neutrinos (ref. [54]).

• Neutrino oscillations provide evidence for the mode entanglement of neutrino mass

eigenstates in a given flavour eigenstate. Given this mode entanglement, it is pertinent

to ask if other quantum correlations are present in neutrino evolution. In this study,

we compute a number of such correlations in the approximation of two flavour neutrino

oscillations. We find that Bell’s inequality is always violated. The various facets of

quantum correlations are very closely tied to the neutrino mixing angle. The point of

minimum survival probability corresponds to the extremum point of all measures of

quantum correlations. This extremum is a maximum for mixing angles below a critical

value and a minimum for above the critical value (ref. [55]).

• Correlations exhibited by neutrino oscillations are studied via quantum information

theoretic quantities. We show that the strongest type of entanglement, genuine mul-

tipartite entanglement, is persistent in the flavour changing states. We prove the exis-

tence of Bell type nonlocal features, in both its absolute and genuine tripartite avatars.

Finally, we show that a measure of nonclassicality, dissension, which is a generalization

of quantum discord to the tripartite case, is nonzero for almost the entire range of

time in the evolution of an initial electron-neutrino. Via these quantum information

44

theoretic quantities capturing different aspects of quantum correlations, we elucidate

the differences between the flavour types, shedding light on the quantum-information

theoretic aspects of the weak force (ref. [56]).

• In the time evolution of neutral meson systems, a perfect quantum coherence is usually

assumed. The important quantities of the B0d system, such as sin 2β and ∆md, are

determined under this assumption. However, the meson system interacts with its

environment. This interaction can lead to decoherence in the mesons even before they

decay. In our formalism this decoherence is modelled by a single parameter λ. It is

desirable to re-examine the procedures of determination of sin 2β and ∆md in meson

systems with decoherence. We find that the present values of these two quantities are

modulated by λ. Re-analysis of B0d data from B-factories and LHCb can lead to a

clean determination of λ, sin 2β and ∆md (ref. [57, 2]).

• We study the geometric phase for neutrinos at various man-made facilities, such as

the reactor and accelerator neutrino experiments. The analysis is done for the three

flavor neutrino scenario, in the presence of matter and for general, noncyclic paths.

The geometric phase is seen to be sensitive to the CP violating phase in the leptonic

sector and the sign ambiguity in ∆31. We find that for experimental facilities where

the geometric phase can complete one cycle, all geometric phase curves corresponding

to different values of CP violating phase, converge to a single point, called the cluster

point. There are two distinct cluster points for positive and negative signs of ∆31. Thus

measurement of geometric phase in these experimental set-ups would help in resolving

the neutrino mass hierarchy problem (ref. [70]).

• We characterize Leggett-Garg-Type Inequality (LGtI) for three flavor neutrino oscil-

lations in the presence of matter and CP violating effects, showing how they can be

expressed in terms of the neutrino survival as well as oscillation probabilities. Hence,

our results are in terms of experimentally measurable quantities. We then explicitly

45

show the violation of LGtI in the context of two ongoing accelerator facilities, NOvA

and T2K. Remarkably, such combinations of two-time correlators are sensitive to the

well-known mass hierarchy problem in ∆31 and also to the CP violation in the leptonic

sector (ref. [71]).

• In this work we study temporal quantum correlations, quantified by Leggett-Garg (LG)

and LG-type inequalities, in the B and K meson systems. We use the tools of open

quantum systems to incorporate the effect of decoherence which is quantified by a

single phenomenological parameter. The effect of CP violation is also included in our

analysis. We find that the LG inequality is violated for both B and K meson systems,

the violation being most prominent in the case of K mesons and least for Bs system.

Since the systems with no coherence do not violate LGI, incorporating decoherence is

expected to decrease the extent of violation of LGI and is clearly brought out in our

results. We show that the expression for the LG functions depends upon an additional

term, apart from the experimentally measurable meson transition probabilities. This

term vanishes in the limit of zero decoherence. On the other hand, the LG-type

parameter can be directly expressed in terms of transition probabilities, making it a

more appropriate observable for studying temporal quantum correlations in neutral

meson systems (ref. [72]).

• Many facets of nonclassicality are probed in neutrino system in the context of three

flavour neutrino oscillations. The analysis is carried out for parameters relevant to two

ongoing experiments NOνA and T2K, and also for the upcoming experiment DUNE.

The various quantum correlations turn out to be sensitive to the mass-hierarchy prob-

lem in neutrinos. This sensitivity is found to be more prominent in DUNE experiment

as compared to NOνA and T2K experiments. This can be attributed to the large

baseline and high energy of the DUNE experiment. Further, we find that to probe

these correlations, the neutrino (antineutrino) beam should be preferred if the sign of

46

mass square difference ∆31 turns out to be positive (negative) (ref. [82]).

• Entropic Leggett-Garg inequality is studied in systems like neutrinos in the context

of two and three flavor neutrino oscillations and in neutral Bd, Bs and K mesons.

The neutrino dynamics is described with the matter effect taken into consideration.

For the decohering B/K meson systems, the effect of decoherence and CP violation

have also been taken into account, using the techniques of open quantum systems.

Enhancement in the violation with increase in the number of measurements has been

found, in consistency with findings in spin-s systems. The effect of decoherence is

found to bring the deficit parameter Dn closer to its classical value zero, as expected.

The violation of entropic Leggett-Garg inequality lasts for a much longer time in K

meson system than in Bd and Bs systems (ref. [83]).

• We study the interplay between coherence and mixedness in meson and neutrino sys-

tems. The dynamics of the meson system is treated using the open quantum system

approach taking into account the decaying nature of the system. Neutrino dynamics is

studied in the context of three flavor oscillations within the framework of a decoherence

model recently used in the context of LSND (Liquid Scintillator Neutrino Detector)

experiment. For meson systems, the decoherence effect is negligible in the limit of zero

CP violation. Interestingly, the average mixedness increases with time for about one

lifetime of these particles. For neutrino system, in the context of the model considered,

the decoherence effect is maximum for neutrino energy around 30 MeV. Further, the

effect of CP violating phase is found to decrease (increase) the coherence in the upper

0 < δ < π (lower π < δ < 2π) half plane (ref. [85]).

• We study various formulations of Leggett-Garg inequality (LGI), specifically, the Wigner

and Clauser-Horne forms of LGI, in the context of subatomic systems, in particular,

three flavor neutrino as well as meson systems. For the neutrinos, some of these

inequalities can be written completely in terms of experimentally measurable proba-

47

bilities. Hence, the Wigner and Clauser-Horne forms of LGI are found to be more

suitable as compared to the standard LGI from the experimental point of view for

the neutrino system. Further, these inequalities exhibit maximum quantum violation

around the energies roughly corresponding to the maximum neutrino flux. The meson

system being inherently a decaying system, allows one to see the effect of decoherence

on the extent of violation of various inequalities. Decoherence is observed to reduce

the degree of violation, and hence the nonclassical nature of the system (ref. [87]).

14 Particle Physics: Signatures of New Physics in the

Flavor Domain

• We consider a model where the standard model is extended by the addition of a vector-

like isosinglet down-type quark d′. We perform a χ2 fit to the flavor physics data

and obtain the preferred central values along with errors of all the elements of the

measurable 3×4 quark mixing matrix. We find that the data constrains |Vtb| ≥ 0.99 at

3σ. Hence, no large deviation in |Vtb| is possible, even if the mixing matrix is allowed to

be non-unitary. The fit also indicates that all the new-physics parameters are consistent

with zero, and the mixing of the d′ quark with the other three is constrained to be

small (ref. [58]).

• The VuQ (vector-singlet up-type quark) model involves the addition of a vector isos-

inglet up-type quark to the standard model. In this model the full CKM quark mixing

matrix is 4 × 3. Using present flavor-physics data, we perform a fit to this full CKM

matrix, looking for signals of new physics (NP). We find that the VuQ model is very

strongly constrained. There are no hints of NP in the CKM matrix, and any VuQ con-

tributions to loop-level flavor-changing b → s, b → d and s → d transitions are very

small. There can be significant enhancements of the branching ratios of the flavor-

changing decays t→ uZ and t→ cZ, but these are still below present detection levels

(ref. [59, 3]).

48

15 Quantum Optics and Quantum Information

• We study number-phase uncertainty in a laser-driven, effectively four-level atomic sys-

tem under electromagnetically induced transparency (EIT) and coherent population

trapping (CPT). Uncertainty is described using (entropic) knowledge of the two com-

plementary variables, namely, number and phase, where knowledge is defined as the

relative entropy with respect to a uniform distribution. The noise produced by ramp-

ing the probe off-resonance is studied in the cases with and without a higher order

nonlinearity due to a 3 − 4′ transition. In both cases, the noise is consistent with

purely dephasing action in the number basis in the CPT as well as EIT regimes. Our

study leads us to the following novel results: We see as a consequence of number-phase

complementarity that the dipole oscillations are correlated in the CPT state, and that

this correlation drops as EIT is approached. The cooperative change in phase with

zero absorption, of coherent light, in a medium formed by atoms in a CPT state can

result in generation of new frequencies whose width depends on amount of cooperation.

The power spectrum of the generated frequencies will depend on whether the atoms

are in CPT or EIT state. Our predictions can explain a recent experimental study.

The Complementarity approach taken easily brings out this difference in CPT and

EIT and helps understand the result our study shows regarding the effect of inclusion

of higher order nonlinearities. We show their presence is detrimental for cooperative

behaviour. Our nonlinear system has properties parallel to the system modelled earlier

by Manassah et. al., and hence can show superradiance. The advantage in our system

is that it is amenable to experiments. CPT and EIT can thus be used in a novel way

to bring about a change in the photon statistics of laser light (ref.[33]).

• Using a kinematic approach we show that the non-adiabatic, non-cyclic, geometric

phase corresponding to the radiation emitted by a three level cascade system pro-

vides a sensitive diagnostic tool for determining the entanglement properties of the

49

two modes of radiation. The nonunitary, noncyclic path in the state space may be

realized through the same control parameters which control the purity/mixedness and

entanglement. We show that the rate of change of the geometric phase reveals its

resilience to fluctuations only for pure Bell type states (ref.[32]).

• The nonclassicality of the two mode photon state generated in a semiclassical, gen-

eralized three-level atomic system, interacting with classical external driving fields is

investigated. The three-level system is considered in any one of the Ξ, Λ or V con-

figuration. The nonclassicality of these two-mode photons can be investigated using

measurement based nonclassical correlations such as measurement induced disturbance,

uantum discord and quantum work deficit. We compare the behavior of these mea-

sures with entanglement (concurrence) and analyze the correlation dynamics at specific

system parameter regimes based on broad observation. We observe, that the qualita-

tive nature of hierarchy of the correlations is dependent on the specificied regime and

configuration. Based on the observations, we comment on how particular configura-

tions are better suited at generating monotonic orrelations at specific regimes and how

the correlation behavior and hierarchy is affected by the population dymanics of the

density matrix (ref. [38]).

• We study nonclassical features in a number of spin-qubit systems including single, two

and three qubit states, as well as an N qubit Dicke model and a spin-1 system, of

importance in the fields of quantum optics and information. This is done by analyzing

the behavior of the well known Wigner, P , and Q quasiprobability distributions on

them. We also discuss the not so well known F function and specify its relation to

the Wigner function. Here we provide a comprehensive analysis of quasiprobability

distributions for spin-qubit systems under general open system effects, including both

pure dephasing as well as dissipation. This makes it relevant from the perspective of

experimental implementation (ref. [51]).

50

• Tomograms are obtained as probability distributions and are used to reconstruct a

quantum state from experimentally measured values. We study the evolution of tomo-

grams for different quantum systems, both finite and infinite dimensional. In realistic

experimental conditions, the quantum states are exposed to the ambient environment

and hence subject to effects like decoherence and dissipation, which are dealt with here,

consistently, using the formalism of open quantum systems. This is extremely relevant

from the perspective of experimental implementation and issues related to state re-

construction in quantum computation and communication. These considerations are

also expected to affect the quasiprobability distribution obtained from experimentally

generated tomograms and nonclassicality observed from them (ref. [52]).

• The possibility of observing nonclassical features in a physical system comprised of

a cavity with two ensembles of two-level atoms has been investigated by considering

different configurations of the ensembles with respect to the Node and Antinode of

the cavity field under the framework of open quantum systems. The study reveals the

strong presence of nonclassical characters in the physical system by establishing the

existence of many facets of nonclassicality, such as the sub-Poissonian boson statis-

tics and squeezing in single modes, intermodal squeezing, intermodal entanglement,

antibunching, and steering. The effect of a number of parameters, characterizing the

physical system, on the different aspects of nonclassicality are also investigated. Specif-

ically, it is observed that the depth of the nonclassicality witnessing parameters can be

enhanced by externally driving one of the ensembles with an optical field. The work

is done in the presence of open system effects, in particular, use is made of Langevin

equations along with a suitable perturbative technique (ref. [79]).

• Nonclassical properties of photon added and subtracted displaced Fock states have

been studied using various witnesses of lower- and higher-order nonclassicality. Com-

pact analytic expressions are obtained for the nonclassicality witnesses. Using those

51

expressions, it is established that these states and the states that can be obtained as

their limiting cases (except coherent states) are highly nonclassical as they show the

existence of lower- and higher-order antibunching and sub-Poissonian photon statistics,

in addition to the nonclassical features revealed through the Mandel QM parameter,

zeros of Q function, Klyshko’s criterion, and Agarwal-Tara criterion. Further, some

comparison between the nonclassicality of photon added and subtracted displaced Fock

states have been performed using witnesses of nonclassicality. This has established that

between the two types of non-Gaussianity inducing operations (i.e., photon addition

and subtraction) used here, photon addition influences the nonclassical properties more

strongly. Further, optical designs for the generation of photon added and subtracted

displaced Fock states from squeezed vacuum state have also been proposed (ref. [84]).

• The interplay between the nonclassical features and the parity-time (PT) symmetry (or

its breaking) is studied here by considering a PT symmetric system consisting of two

cavities with gain and loss. The conditions for PT invariance is obtained for this system.

The behavior of the average photon number corresponding to the gain and loss modes

for different initial states (e.g., vacuum, NOON, coherent, and thermal states) has also

been obtained. With the help of the number operators, quantum Zeno and anti-Zeno

effects are studied, and the observed behavior is compared in PT symmetric (PTS)

and PT symmetry broken (PTSB) regimes. It has been observed that the relative

phase of the input coherent fields plays a key role in the occurrence of these effects.

Further, some nonclassicality features are witnessed using criteria based on the number

operator(s). Specifically, intermodal antibunching, sum and difference squeezing, are

investigated for specific input states. It is found that the various nonclassical features,

including the observed quantum Zeno and anti-Zeno effects, are suppressed when one

goes from PTS to PTSB regime. In other words, the dominance of the loss/gain rate

in the field modes over the coupling strength between them diminishes the nonclassical

features of the system (ref. [86]).

52

16 Quantum Games

• We present a new form of a Parrondo game using discrete-time quantum walk on a

line. The two players A and B with different quantum coins operators, individually

losing the game can develop a strategy to emerge as joint winners by using their coins

alternatively, or in combination for each step of the quantum walk evolution. We also

present a strategy for a player A (B) to have a winning probability more than player B

(A). Significance of the game strategy in information theory and physical applications

are also discussed (ref.[29]).

17 Non-Linear Dynamics

• A new q-deformed logistic map is proposed and it is found to have concavity in parts of

the x-space. Its one-cycle and two-cycle non-trivial fixed points are obtained which are

found to be qualitatively and quantitatively different from those of the usual logistic

map. The stabilty of the proposed q-logistic map is studied using Lyapunov exponent

and with a change in the value of the deformation parameter q, one is able to go from

the chaotic to regular dynamical regime. The implications of this q-logistic map on

Parrondo’s paradox are examined (ref.[25]).

• The delay logistic map with two types of q–deformations: Tsallis and Quantum–group

type are studied. The stability of the map and its bifurcation scheme is analyzed as a

function of the deformation and delay feedback parameters. Chaos is suppressed in a

certain region of deformation and feedback parameter space. The steady state obtained

by delay feedback is maintained in one type of deformation while chaotic behavior is

recovered in another type with increasing delay (ref.[34]).

53

18 Generalized Thermodynamics

• We investigate the most general meaning of intrinsic Riemannian geometry for com-

plex systems from the perspective of statistical mechanics and associated probability

distributions. The entropic formulation of statistical mechanics is the ingredient which

enables a connection between statistical mechanics and the corresponding Riemannian

geometry. The form of the entropy used commonly is the Shannon entropy. How-

ever, for modelling complex systems it is often useful to make use of higher entropies

such as the Renyi and Tsallis entropies. We consider Shannon, Renyi and Tsallis en-

tropies for our analysis. We focus on the one, two and the three particle thermally

excited configurations. We find that statistical pair correlation functions associated

with Gibbs-Shannon, Renyi and Tsallis configurations have well defined definite ex-

pressions, which may be extended for arbitrary finite particle systems. In either case,

we find a well defined intrinsic Remannian manifold. In particular, any finite particle

Renyi and Tsallis configurations always correspond to an interacting statistical sys-

tem. On the other hand, the Gibbs-Shannon system corresponds to a non-interactiing

statistical configuration. Moreover, the underlying statistical configurations associated

with Renyi and Tsallis systems become ill-defined at the extreme value of the Renyi

parameter, q = 1 while the Gibbs-Shannon remains intact (ref.[36]).

• It is found that Tsallis and Renyi entropies are suited in modeling complex systems

where long range correlations play an important role in a description of the system

dynamics. These entropies form a q generalization of the well known Shannon entropy

to which they reduce to in the limit of q −→ 1. The q serves as a scaling parameter en-

abling the system to sample, not necessarily, neighbouring points. These issues are inti-

mately connected to quantum groups. Here we propose a two-parameter generalization

of these entropies, to which they reduce to in the limit of one of the parameters tending

to one. The basic tool is a two-parameter difference operator acting on an appropriate

54

generating function. From this one attains a family of generalized entropies including

a two-parameter generalization of the Renyi entropy. Taking appropriate limits, many

other entropies known in the literature are recovered. From the two-parameter Renyi

one can recover the two-parameter Tsallis entropy by expanding the logarithmic terms

in the Renyi entropy and keeping only the linear term. This two-parameter difference

operator has its origin in the corresponding two-parameter generalization of quantum

groups. We make a number of applications of these generalized entropies (ref.[37]).

Publications: Journal Publications

1. “Quantum theory of a Stern-Gerlach system in contact with a lineraly dissipative

environment”

S. Banerjee and R. Ghosh, Physical Review A: 62, 042105 (2000).

2. “Propagator for a spin-Bose system with the Bose field coupled to a reservoir of har-

monic oscillators”

S. Banerjee and R. Ghosh, J. Phys. A: Math. Gen: 36, 5787 (2003).

3. “General quantum Brownian motion with initially correlated and nonlineraly coupled

environment”

S. Banerjee and R. Ghosh, Physical Review E.: 67, 056120 (2003).

4. “Decoherence and dissipation of an open quantum system with a squeezed and fre-

quency modulated heat bath”

S. Banerjee, Physica A: 337, 67 (2004).

5. “Ultracoherence and Canonical Transformations”

J. Kupsch and S. Banerjee, Infinite Dimensional Analysis, Quantum Probability and

Related Topics: 9, 413 (2006), eprint: arXiv:math-ph/0410049.

6. “Applications of Canonical Transformations”

55

S. Banerjee and J. Kupsch, J. Phys. A: Math. Gen 38, 5237 (2005), eprint: arXiv:quant-

ph/0410209.

7. “Structure of Propagators for quantum nondemolition systems”

S. Banerjee and R. Ghosh, eprint: arXiv:quant-ph/0611125.

8. “Functional integral treatment of some quantum nondemolition systems and their vari-

ants”

S. Banerjee and R. Ghosh, J. Phys. A: Math. Theo.: 40, 1273 (2007), eprint:arXiv:quant-

ph/0611127.

9. “Dynamics of decoherence without dissipation in a squeezed thermal bath”

S. Banerjee and R. Ghosh, J. Phys. A:Math. Theo: 40, 13735 (2007), eprint:

arXiv:quant-ph/0703054.

10. “Classical limit of master equation for harmonic oscillator coupled to oscillator bath

with separable initial conditions”

S. Banerjee and A. Dhar, Physical Review E: 73, 067104 (2006), eprint: arXiv:cond-

mat/0511645.

11. “Phase diffusion pattern in quantum nondemolition systems”

S. Banerjee, J. Ghosh and R. Ghosh, Phys. Rev. A: 75, 062106 (2007), eprint:arXiv:quant-

ph/0703055.

12. “Geometric Phase of a qubit interacting with a squeezed-thermal bath”

S. Banerjee and R. Srikanth, Eur. Phys. J. D: 46, 335 (2008), eprint: arXiv:quant-

ph/0611161.

13. “An environment-mediated quantum deleter”

R. Srikanth and S. Banerjee, Phys. Lett. A: 367, 295 (2007), eprint: arXiv:quant-

ph/0611263.

56

14. “ Phase diffusion in quantum dissipative systems”

S. Banerjee and R. Srikanth, Phys. Rev. A: 76, 062109 (2007), eprint:arXiv:0706.3633.

15. “ Complementarity in atomic systems: an information-theoretic approach”

R. Srikanth and S. Banerjee, Eur. Phys. J. D: 53, 217 (2009), eprint: arXiv:0711.0875.

16. “Complementarity in generic open quantum systems”

S. Banerjee and R. Srikanth, Modern Phys. Lett. B: 24, 2485 (2010), eprint: arXiv:0905.3269.

17. “Complementarity in atomic and oscillator systems”

R. Srikanth and S. Banerjee, Phys. Lett. A: 374, 3147 (2010), eprint:arXiv: 1005.3456.

18. “ Symmetries and noise in quantum walk”

C. M. Chandrashekar, R. Srikanth and S. Banerjee, Phys. Rev. A: 76, 022316 (2007),

eprint: arXiv:quant-ph/0607188.

19. “Symmetry-noise interplay in quantum walk on n-cycle”

S. Banerjee, R. Srikanth, C. M. Chandrashekar and Pranaw Rungta, Phys. Rev. A:

78, 052316 (2008), eprint: arXiv:0803.4453.

20. “ The squeezed generalized amplitude damping channel”

R. Srikanth and S. Banerjee, Phys. Rev. A: 77, 012318 (2008), eprint:arXiv:0707.0059.

21. “Entanglement dynamics in two-qubit open quantum system interacting with a squeezed

thermal bath via quantum nondemolition interaction”

S. Banerjee, V. Ravishankar and R. Srikanth, Euro. Phys. J. D: 56, 277 (2010),

eprint:arXiv:0810.5034.

57

22. “ Dynamics of entanglement in two-qubit open quantum system interacting with a

squeezed thermal bath via dissipative interaction”

S. Banerjee, V. Ravishankar, R. Srikanth, Ann. of Phys. (NY).: 325, 816 (2010),

eprint:arXiv:0901.0404 .

23. “Geometric phase in a two-qubit system interacting with a bath via quantum non-

demolition as well as dissipative interactions”

S. Banerjee and R. Srikanth, work in progress.

24. “Relationship Between Quantum Walk and Relativistic Quantum Mechanics”

C. M. Chandrashekar, S. Banerjee and R. Srikanth, Phys. Rev. A: 81, 062340 (2010),

eprint: arXiv:1003.4656.

25. “A q-deformed logistic map and its implications”

S. Banerjee and R. Parthasarathy, J. Phys. A.:Math. Theor.: 44, 045104 (2011),

eprint:arXiv:1003.0183.

26. “A study of Quantum Correlations in Open Quantum Systems”

I. Chakrabarty, S. Banerjee and N. Siddharth, Quantum Information and Computation:

11, 0541 (2011), eprint:arXiv:1006.1856.

27. “Quantumness in decoherent quantum walk using measurement-induced disturbance”

R. Srikanth, S. Banerjee and C. M. Chandrashekar, Phys. Rev. A: 81, 062123 (2010),

eprint:arXiv:1005.3456.

28. “Entanglement generation in spatially separated systems using quantum walk”

C. M. Chandrashekar, S. K. Goyal and S. Banerjee, Journal of Quantum Information

Science: 2, 15 (2012), eprint:arXiv:1005.3785.

29. “Parrondo’s game using a discrete-time quantum walk”

C. M. Chandrashekar and S. Banerjee, Phys. Lett. A: 375, 1553 (2011), arXiv:1008.5121.

58

30. “Quantumness of noisy quantum walks: a comparison between measurement-induced

disturbance and quantum discord”

B. R. Rao, R. Srikanth, C. M. Chandrashekar and S. Banerjee, Phys. Rev. A: 83,

064302 (2011), eprint:arXiv:1012.5040.

31. “Effect of control procedures on the evolution of entanglement in open quantum sys-

tems”

S. Goyal, S. Banerjee and S. Ghosh, Phys. Rev. A: 85, 012327 (2012), eprint:arXiv:1102.4403.

32. “Geometric Phase: An Indicator of Entanglement”

S. N. Sandhya and S. Banerjee, Euro. Phys. J. D: 66, 168 (2012), eprint:arXiv:1103.2587.

33. “An information theoretic study of number-phase uncertainty in a four level atomic

system”

A. Sharma, R. Srikanth, S. Banerjee and H. Ramachandran, arXiv:1108.0641.

34. “q–deformed logistic map with delay feedback”

M. D. Shrimali and S. Banerjee, arXiv:1203.3137; Commun. Nonlinear Sci. Numer.

Simulat (CNSNS) 18, 3126 (2013).

35. “The quantum cryptographic switch”

S Narayanaswamy, O Srikrishna, R Srikanth, S. Banerjee and A. Pathak, arXiv:1111.4834;

Quantum Information Processing, Special Issue on Quantum Cryptography 13, 59

(2014).

36. “A thermodynamic geometric study of Renyi and Tsallis entropies”

B. N. Tiwari, V. Chandra and S. Banerjee, arXiv:1008.2853.

37. “A family of generalized entropies”

R. Jagannathan and S. Banerjee, work in progress.

59

38. “Investigating nonclassical correlations of radiation emitted from generalized three-

level atomic systems”

H. S. Dhar, S. Banerjee, A. Chatterjee and R. Ghosh, Ann. of Phys. 331, 97 (2013),

arXiv:1205.5665.

39. “Laplacian matrices of weighted digraphs represented as quantum states”, Quantum

Information Processing 16, 1-22 (2017) : Eprint:arXiv:1205.2747: Bibhas Adhikari,

Subhashish Banerjee, Satyabrata Adhikari and Atul Kumar.

40. “Dissipative and Non-dissipative Single-Qubit Channels: Dynamics and Geometry”

S. Omkar, R. Srikanth and S. Banerjee, Quantum Information Processing 12, 3725

(2013), arXiv:1207.7226.

41. “An Operational Meaning of Discord in terms of Teleportation Fidelity”

S. Adhikari and S. Banerjee, Phys. Rev. A 86, 062313 (2012), arXiv:1207.7226.

42. “Quantification of Entanglement of Teleportation in Arbitrary Dimensions”

Sk Sazim, S. Adhikari, S. Banerjee and T. Pramanik, Quantum Information Processing

13, 863 (2014), arXiv:1208.4200.

43. “Enhancement of Geometric Phase by Frustration of Decoherence: A Parrondo like

Effect”

S. Banerjee, C. M. Chandrashekar and A. K. Pati, Phys. Rev. A 87, 042119 (2013),

arXiv:1208.5563.

44. “The operator sum-difference representation for quantum maps: application to the

two-qubit amplitude damping channel”

S. Omkar, R. Srikanth and S. Banerjee, Quantum Information Processing 14, 2255

(2015), doi:10.1007/s11128-015-0965-5, arXiv:1212.2780.

45. “Decoherence free B d and B s meson systems”

A. K. Alok and S. Banerjee, Phys. Rev. D 88, 094013 (2013), arXiv:1304.4063.

60

46. “Entanglement in the Grovers Search Algorithm” S. Chakraborty, S. Banerjee, S. Ad-

hikari and A. Kumar, arXiv:1305.4454.

47. “Quantum code for quantum error characterization”, S. Omkar, R. Srikanth and S.

Banerjee, Phys. Rev. A 91, 052309 (2015).

48. “Characterization of quantum dynamics using quantum error correction”, S. Omkar,

R. Srikanth and S. Banerjee, Phys. Rev. A 91, 012324 (2015), Eprint:arXiv:1405.0964.

49. “A graph theoretical approach to states and unitary operations”, Quantum Information

Processing 15, 2193 (2016); Eprint:arXiv:1502.07821: Supriyo Dutta, Bibhas Adhikari,

Subhashish Banerjee.

50. “Controlled bidirectional remote state preparation in noisy environment: A generalized

view”, Quantum Information Processing 14, 3441 (2015), doi:10.1007/s11128-015-1038-

5: Eprint:arXiv:1492.0833: V. Sharma, C. Shukla, S. Banerjee and A. Pathak.

51. “Quasiprobability distributions in open quantum systems: spin-qubit systems”, Ann.

of Phys. 362, 261286 (2015), Kishore Thapliyal, Subhashish Banerjee, Anirban Pathak,

S. Omkar, V. Ravishankar.

52. “Tomograms for open quantum systems: in(finite) dimensional optical and spin sys-

tems”: Ann. of Phys. 366, 148 (2016); arXiv:1507.02135: Kishore Thapliyal, Sub-

hashish Banerjee, Anirban Pathak.

53. “The Unruh effect interpreted as a quantum noise channel”, Quantum Information and

Computation (QIC) 16, 0757 (2016); Eprint:arXiv:1408.1477: S. Omkar, S. Banerjee,

R. Srikanth and A. K. Alok.

54. “Quantum correlations in B and K meson systems”, Eur. Phys. J. Plus 131, 129

(2016); Eprint:arXiv:1409.1034: S. Banerjee, A. K. Alok and R. MacKenzie.

61

55. “Quantum correlations in two-flavor neutrino oscillations”, Nucl. Phys. B 909, 65

(2016); Eprint:arXiv:1411.5536: A. K. Alok, S. Banerjee and S. U. Sankar.

56. “A quantum information theoretic analysis of three flavor neutrino oscillations”: Euro-

pean Physical Journal C (EPJC) 75, 487 (2015); arXiv:1508.03480: Subhashish Baner-

jee, Ashutosh Kumar Alok, R. Srikanth and Beatrix C. Hiesmayr.

57. “Re-examining sin(2beta) and Delta m(d) from evolution of B(d) mesons with deco-

herence”, Phys. Lett. B 749, 94 (2015): Ashutosh Kumar Alok, Subhashish Banerjee

and S. Uma Sankar.

58. “Constraining quark mixing matrix in isosinglet vector-like down quark model from a

fit to flavor-physics data”, Nucl. Phys. B 906, 321 (2016); Eprint:arXiv:1402.1023: A.

K. Alok, S. Banerjee, D. Kumar and S. U. Sankar.

59. “New-physics signals of a model with a vector-singlet up-type quark”, Phys. Rev. D

92, 013002 (2015): Ashutosh Kumar Alok, Subhashish Banerjee, Dinesh Kumar, S.

Uma Sankar and David London.

60. “Quantum Fisher and Skew information for Unruh accelerated Dirac qubit”: Eur.

Phys. J. C (EPJC) 76, 437 (2016); arXiv:1511.03029: Subhashish Banerjee, Ashutosh

Kumar Alok and S. Omkar.

61. “The two-qubit amplitude damping channel: characterization using quantum stabilizer

codes”: Ann. of Phys. 373, 145 (2016); arXiv:1511.03368: S. Omkar, R. Srikanth,

Subhashish Banerjee and Anil Shaji.

62. “Evolution of coherence and non-classicality under global environmental interaction ”:

Quantum Information Processing 17, 236 (2018); arXiv:1601.04742: Samyadeb Bhat-

tacharya, Subhashish Banerjee and Arun Kumar Pati.

62

63. “Bipartite separability and non-local quantum operations on graphs ”: Phys. Rev.

A 94, 012306 (2016); arXiv:1601.07704: Supriyo Dutta, Bibhas Adhikari, Subhashish

Banerjee and R. Srikanth.

64. “A comparative study of protocols for secure quantum communication under noisy en-

vironment: single-qubit-based protocols versus entangled-state-based protocols”: Quan-

tum Information Processing 15, 4681 (2016), DOI 10.1007/s11128-0016-1396-7; arXiv:1603.00178:

Vishal Sharma, Kishore Thapliyal, Anirban Pathak and Subhashish Banerjee.

65. “Characterization of Unruh Channel in the context of Open Quantum Systems”: Jour-

nal of High Energy Physics (JHEP) 02, 82 (2017), DOI: 10.1007/JHEP02(2017);

arXiv:1603.05450: Subhashish Banerjee, Ashutosh Kumar Alok, S. Omkar and R.

Srikanth.

66. “Quantum cryptography over non-Markovian channels”: Quantum Information Pro-

cessing, 16, 115 (2017), DOI: 10.1007/s11128-017-1567-1; arXiv:1608.06071: Kishore

Thapliyal, Anirban Pathak and Subhashish Banerjee.

67. “Seidel switching for weighted multi-digraphs and its quantum perspective”: arXiv:1608.07830:

Supriyo Dutta, Bibhas Adhikari and Subhashish Banerjee.

68. “Quantum discord of states arising from graphs” Quantum Information Processing,

16(8), 183 (2017), arXiv:1702.06360: Supriyo Dutta, Bibhas Adhikari, Subhashish

Banerjee.

69. “Zero discord quantum states arising from weighted digraphs”: arXiv:1705.00808:

Supriyo Dutta, Bibhas Adhikari, Subhashish Banerjee.

70. “Geometric phase and neutrino mass hierarchy problem”: J. Phys. G, 45, 085002

(2018), arXiv:1703.09894: Khushboo Dixit, Ashutosh Kumar Alok, Subhashish Baner-

jee and Dinesh Kumar.

63

71. “Legget-Garg-Type inequalities and the neutrino mass-degeneracy problem”: to ap-

pear in Nuclear Physics B, arXiv:1710.05562: Javid Naikoo, Ashutosh Kumar Alok,

Subhashish Banerjee, S. Uma Sankar, Giacomo Guarnieri, Christiane Schultze, Beatrix

C. Hiesmayr.

72. “Study of temporal quantum correlations in decohering B and K meson systems”:

Phys. Rev. D 97, 053008 (2018); arXiv:1802.04265: Javid Naikoo, Ashutosh Kumar

Alok, Subhashish Banerjee.

73. “Non-Markovian Dynamics of Discrete-Time Quantum Walks”: arXiv:1703.08004: Sub-

hashish Banerjee, N. Pradeep Kumar, R. Srikanth, Vinayak Jagadish and Francesco

Petruccione.

74. “Non-Markovian evolution: a quantum walk perspective”: Open Systems and Infor-

mation Dynamics (OSID) 25, 1850014 (2018); arXiv:1711.03267: Pradeep Kumar,

Subhashish Banerjee, R. Srikanth, Vinayak Jagadish and Francesco Petruccione.

75. “Thermodynamics of non-Markovian reservoirs and heat engines”: Phys. Rev. E

97, 062108 (2018): arXiv:1801.00744v1: George Thomas, Nana Siddharth, Subhashish

Banerjee and Sibasish Ghosh. .

76. “Enhanced non-Markovian behavior in quantum walks with Markovian disorder”: Sci-

entific Reports 8, 8801 (2018); DOI:10.1038/s41598-018-27132-7arXiv:1802.05478: arXiv:1802.05478:

N. Pradeep Kumar, Subhashish Banerjee and C. M. Chandrashekar.

77. “Analysis of atmospheric effects on satellite based quantum communication: A compar-

ative study”: accepted for publication in Quantum Information Processing: arXiv:1711.08281:

Vishal Sharma and Subhashish Banerjee.

78. “Decoherence can help quantum cryptographic security”: Quantum Information Pro-

cessing, 17, 207 (2018), arXiv:1712.06519: Vishal Sharma, U. Shrikant, R. Srikanth

and Subhashish Banerjee.

64

79. “Probing nonclassicality in an optically-driven cavity with two atomic ensembles”:

Phys. Rev. A 97, 063840 (2018); arXiv:1712.04154: Javid Naikoo, Kishore Thapliyal,

Anirban Pathak and Subhashish Banerjee.

80. “Non-Markovian dephasing and depolarizing channels”: Phys. Rev. A 98, 032328

(2018); arXiv:1805.11411: U. Shrikant, R. Srikanth and Subhashish Banerjee.

81. “Leggett-Garg inequality violation under non-Markovian noise”: arXiv:1806.00537:

Javid Naikoo, Subhashish Banerjee and R. Srikanth.

82. “Quantum correlations and the neutrino mass degeneracy problem”: Eur. Phys. J. C

78, 914 (2018), arXiv:1807.01546: Khushboo Dixit, Javid Naikoo, Subhashish Banerjee

and Ashutosh Kumar Alok.

83. “Entropic Leggett-Garg inequality in neutrinos and B (K) meson systems”: Eur. Phys.

J. C 78, 602 (2018): Javid Naikoo and Subhashish Banerjee.

84. “Lower- and higher-order nonclassical properties of photon added and subtracted dis-

placed Fock states”: Annalen der Physik (Berlin) 531, 1800318 (2019); arXiv:1808.01458:

Priya Malpani, Nasir Alam, Kishore Thapliyal, Anirban Pathak, V. Narayanan and

Subhashish Banerjee.

85. “Study of coherence and mixedness in meson and neutrino systems”: Eur. Phys. J. C

79, 96 (2019); arXiv:1809.09947: Khushboo Dixit, Javid Naikoo, Subhashish Banerjee

and Ashutosh Kumar Alok.

86. “Quantum Zeno effect and nonclassicality in a PT symmetric system of coupled cav-

ities”: arXiv:1811.05604: Phys. Rev. A 99, 023820 (2019): Javid Naikoo, Kishore

Thapliyal, Subhashish Banerjee, Anirban Pathak.

87. “Probing inequivalent forms of Legget-Garg inequality in subatomic systems ”: arXiv:1906.05995:

Javid Naikoo, Swati Kumari, Subhashish Banerjee, A. K. Pan.

65

88. “Leggett-Garg inequality in the context of three flavour neutrino oscillation”: Phys.

Rev. D 99, 095001 (2019): Javid Naikoo, Ashutosh Kumar Alok, Subhashish Banerjee,

S. Uma Sankar.

89. “Facets of quantum information under non-Markovian evolution”: Phys. Rev. A 99,

042128 (2019): Javid Naikoo, Supriyo Dutta, Subhashish Banerjee.

90. “Interplay between nonclassicality and PT symmetry in an effective two level system

with open system effects”: Phys. Rev. A 100, 023836 (2019), arXiv:1904.11181: Javid

Naikoo, Subhashish Banerjee, Anirban Pathak.

91. “Quantum correlations in neutrino oscillations in curved spacetime”: Phys. Rev.

D 100, 055021 (2019), arXiv:1903.05664: Khushboo Dixit, Javid Naikoo, Banibrata

Mukhopadhyay, Subhashish Banerjee.

92. “Quantum phase properties of photon added and subtracted displaced Fock states”:

Annalen der Physik (Berlin) 31 (11), (2019), arXiv:1904.01603: Priya Malpani, Kishore

Thapliyal, Nasir Alam, Anirban Pathak, V. Narayanan, Subhashish Banerjee. (Paper

appeared on the coverpage of the November issue of the journal.)

93. “Impact of photon addition and subtraction on nonclassical and phase properties of a

displaced Fock state”: to appear in Optics Communications, arXiv:1908.04086 : Priya

Malpani, Kishore Thapliyal, Nasir Alam, Anirban Pathak, V. Narayanan, Subhashish

Banerjee.

94. “Manipulating nonclassicality via quantum state engineering processes: Vacuum filtra-

tion and single photon addition”: to appear in Annalen der Physik (Berlin), arXiv:1907.03257:

Priya Malpani, Nasir Alam, Kishore Thapliyal, Anirban Pathak, V. Narayanan, Sub-

hashish Banerjee.

95. “Legget-Garg-Type inequalities and the neutrino mass-degeneracy problem”: to ap-

pear in Nuclear Physics B, Javid Naikoo, Ashutosh Kumar Alok, Subhashish Banerjee,

66

S. Uma Sankar, Giacomo Guarnieri, Christiane Schultze, Beatrix C. Hiesmayr.

96. “A study of coherence based measure of quantumness in (non) Markovian channels”:

to appear in Quantum Information Processing, arXiv:1905.12872: Javid Naikoo, Sub-

hashish Banerjee.

97. “Violation of Leggett-Garg type inequalities in a driven two level atom interacting with

a squeezed thermal reservoir”: to appear in Phys. Rev. A: arXiv:1908.04054: Javid

Naikoo, Subhashish Banerjee, Arun M. Jayannavar.

98. “Current Trends in Quantum Optics”: arXiv:1902.08576: Subhashish Banerjee, Arun

Jayannavar.

99. “Quantum Communication using Code Division Multiple Access Network”: arXiv:1905.12829:

Vishal Sharma, Subhashish Banerjee.

100. “Local description of S-matrix in quantum field theory in curved spacetime using

Riemann-normal coordinate”: arXiv:1908.06717: Susobhan Mandal, Subhashish Baner-

jee.

101. “Response of a uniformly accelerated Unruh-DeWitt detector in polymer quantiza-

tion”: arXiv:1909.01027 : Gopal Sardar, Subhashish Banerjee.

102. “On a concept of quantum non-Markovianity weaker than CP-indivisibility”: arXiv:1911.04162:

U. Shrikant, R. Srikanth, Subhashish Banerjee.

103. “Quantumness of channels”: arXiv:1911.07677: Javid Naikoo, Subhashish Banerjee,

R. Srikanth.

Publications: Conference Publications

1. “An Invitation to Open Quantum Systems Applied to Quantum Information” S. Baner-

jee, Proceedings of National Conference on Quantum Correlations: Foundations and

67

Applications, organized by Department of Physics, Vidyasagar College for Women,

Kolkata along with Physics and Applied Mathematics Unit, Indian Statistical Insti-

tute, Kolkata .

2. “Effect of decoherence on clean determination of sin(2β) and ∆md” Ashutosh Kumar

Alok, Subhashish Banerjee and S. Uma Sankar; PoS (Proceedings of Science) EPS-

HEP2015 (2015) 578 .

3. “New-physics signals of a model with an isosinglet vector-like t′ quark” Ashutosh Ku-

mar Alok, Subhashish Banerjee, Dinesh Kumar, S. Uma Sankar and David London;

PoS (Proceedings of Science) EPS-HEP2015 (2015) 579 .

4. “Analysis of Quantum Key Distribution based Satellite Communication” Vishal Sharma,

Subhashish Banerjee; in 2018 9th International Conference on Computing, Communi-

cation and Networking Technologies (ICCCNT) 2018 Jul 10 (pp. 1-5). IEEE, DOI:

10.1109/ICCCNT.2018.8494189.; arXiv:1807.07544.

Publications: Book Chapters

1. “Principles and Applications of Free Space Optical Communication”, Authors: Vishal

Sharma, Subhashish Banerjee and Bazil Raj; ISBN: 978-1-78561-415-6 (https://www.theiet.org/resources/books/telecom/free-

space.cfm).

Publications: Monographs

1. A Thermodynamic Geometric Study of Complex Entropies

B. N. Tiwari, V. Chandra and S. Banerjee, Lap Lambert Academic Publishing (2011).

2. A Study of Dynamics of Open Quantum Systems

S. Banerjee, Lap Lambert Academic Publishing (2011).

Publications: Books

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1. Open Quantum Systems: Dynamics of Nonclassical Evolution

Subhashish Banerjee, Springer and Hindustan Book Agency; ISBN 978-981-13-3181-7,

ISBN 978-981-13-3182-4 (eBook), https://doi.org/10.1007/978-981-13-3182-4.

Awards:

Awarded the “Science Foundation Ireland Short Term Travel Fellowship” from May 1 2012

to July 31 2012.

Projects:

(a). Co-Principal Investigator in the CSIR funded project on “Hunting of new physics

through b→ s transitions”. Project completed;;

(b). Principal Investigator in the CSIR funded project on “Graph Theoretical Aspects in

Quantum Information Processing”. Project completed;

(c). Principal Investigator in the CSIR funded project on “A Study of Quantum Correla-

tions: Squeezing and its various facets”. Project ongoing;

(d). Principal Investigator, from the Indian side, in the “DST India-BMWfW Austria Project

Based Personnel Exchange Programme for 2017-2018”, titled “Probing the Foundations of

Quantum Mechanics in Neutrino Oscillations”. Project completed.

(e). Co-Principal Investigator in the QuEST (Quantum Enabled Science and Technol-

ogy) project: Interdisciplinary Cyber Physical Systems (ICPS)programme of DST Grant

No.:DST/ICPS/QuST/Theme-1/2019/13 “Quantum heat engines”. Project ongoing;

(f). Co-Principal Investigator in the QuEST (Quantum Enabled Science and Technol-

ogy) project: Interdisciplinary Cyber Physical Systems (ICPS) programme of DST Grant

No.:DST/ICPS/QuST/Theme-1/2019/6 “Generation of entangled photons and its applica-

tions to Quantum Computation and Information Processing”. Project ongoing.

Students:

A. Undergraduate:

1. Guided B. Tech. Project of Jothishwaran C. Arunagiri, IIT Jodhpur, titled “Towards

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a better understanding of the Josephson Qubits” (2013).

2. Guided B. Tech. Project of Amar Singh Saini, IIT Jodhpur, titled “Quantum Cryp-

tography (Quantum Repeater Technology)” (2014).

3. Guided Summer Internship Project of Ravi and Pradeep Saran, IISER Bhopal, titled

“Quantum Computing and Information” (2014).

4. Guided Summer Internship Project of Rakesh Saini, IIT ISM DHANBAD, on Quna-

tum Field Theory (2019).

5. Guided Summer Internship Project of Smit Chaudhary, IIT Kanpur, on Quantum

Optics (2019).

B. Postgraduate:

1. Guided the Masters (M.Tech.) Thesis of Shantanav Chakraborty, IIT Jodhpur, titled

“Entanglement in the Quantum Search Algorithm”.

2. Guided the MSc Thesis of Nidhin Sathyan, IIT Jodhpur, titled “Studies on Quantum

Entanglement”.

3. Guided the MSc Thesis of Vikrant Chaudhary, IIT Jodhpur, titled “Photon Localiza-

tion”.

4. Guided the M.Tech training project for 8 th Semester of Komal Varshney, a student

of B.Tech - M.Tech 4 th year at Centre for Converging Technologies, University of

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Rajasthan (UOR), Jaipur titled Quantum Cryptography.

5. Guided the MSc Thesis of Ekta Panwar, IIT Jodhpur, titled “Quantum speed limits

in physical processes”.

C. Ph.D:

1. Vibha Sahlot: Thesis successfully defended. Thesis title “Conflicts in Geometry”.

2. Supriyo Dutta: Thesis successfully defended. Thesis title “Graph Theoretic Aspects of

Quantum Information Processing”.

3. Vishal Sharma: Thesis successfully defended. Thesis title “Quantum communication

under noisy environment: from Theory to Applications”.

4. Javid Ahmad Naikoo: Thesis ongoing.

Additional:

(a). Invited reviewer for Mathematical Reviews (MR);

(b). Reviewer for J. of Stat. Phys;

(c). Reviewer for J. Phys. A;

(d). Reviewer for J. Phys. B;

(e). Reviewer for Physica A;

(f). Reviewer for QIC and QIP;

(g). Reviewer for Pramana;

(h). Reviewer for Phys. Rev. A;

(i). Reviewer for Phys. Rev. D.

(j). Reviewer of two thesis.

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