Practical Aspects of Quantum Information Imperial College London Martin Plenio Department of Physics...

Practical Aspects of Quantum Information

Imperial College London

Martin PlenioDepartment of Physics

and

Institute for Mathematical Sciences

Imperial College Londonwww.imperial.ac.uk/quantuminformation

Imperial College London Imperial, 11th July 2006

The IMS Team

Martin Plenio, Programme Leader

Jens Eisert, EurYI fellow

Shashank Virmani

Postdocs:

Moritz Reuter

PhD students:

Koenraad Audenaert

Christopher Dawson

Michael Hartmann

Philip Hyllus

Kenneth Pregnell

Alexander Retzker

Alessio Serafini

Fernando Brandão

Oscar Dahlsten

Alvaro Feito

David Gross

Konrad Kieling

+ Affiliated Groups of: Peter Knight Terry RudolphStefan Scheel

Danny TernoFrom October 2006

Matthew LakeFrom October 2006

Marcus CramerFrom October 2006


QIT Methods in Many Body Physics

Formal Theory of Entanglement and its

Properties

Application OrientedTheory

Areas of Interest

Implementations in: Ion traps, Cavity QED, Photonic Systems, Nano-mechanical Oscillators, Photonic Crystals

Entanglement: Characterization, Manipulation, Quantification, Witnesses & CriteriaMath. Found. of QMModels of Computation

Apply QIT to: Scaling Laws, Simulation Methods, Dynamics, Critical Systems, Emulating Hamiltonians, Geometric Phases

Concepts: Linear Optics Quantum Computation, Manipulation by Propagation, Entanglement Generation by Measurement


Projective Measurements

Projective Measurement

That’s what you learned in your quantum mechanics course!

… and we cannot be more general than that !?

Yes and No !


Generalized Measurements

Ancilla



Apply joint unitary operationto correlate systems.

Ancilla



Projective Measurement on Ancilla:


Generalized Measurements in Quantum Optical Systems


Spontaneous emission: Observation of a decaying atom

Initial state:

eg eeg t

State after no-click at time t:

No detection ever Atom in ground state

g

Each failure to detect provides information quantum state changes!


Ingredients:• Spontaneous decay• Interaction between atoms

Idea: take two atoms in an optical cavity

Symmetrical positions

M.B. Plenio, S.F. Huelga, A. Beige, P.L. Knight, Phys. Rev. A 59, 2468 (1999)

Photons may leakout of the mirrors

Use no-detection events to create entanglement


Creating entanglement in a lossy cavity


Now we wait and see …

Creating entanglement in a lossy cavity


No photon detected

)22

(2

1 vac

geegvac

geeg

vacegini

In 50% of the cases we will never see a photon singlet state

vacgeeg

ini

2

One photon detected

photonggini

ge eg

gg

ee


Imperfect detector registers ‘no-click’

• No photon has leaked out of the cavity

• A photon has left the cavity but has been missed by the detector

Resulting partially entangled state is of the form:

Detector efficiency = p


Many photons will be emitted

No photons will be emitted

Detector will see some photons after sufficiently long time

When no photons are seen, success prob = p

M.B. Plenio, S.F. Huelga, A. Beige, P.L. Knight, Phys. Rev. A 59, 2468 (1999)


Generalized measurements on distant particles


dcbaba vaccvacba 01)(

2

1

2

0110

dcbaba vacdvacba 10)(

2

1

2

0110

Beamsplitters make Bell projections


Bell projection allows entanglement swapping

Bell projectiononto

Goal: Entangle Atoms with photons Make Bell projection on photons

Obtain entangled atoms


S. Bose, P.L. Knight, M.B. Plenio and V. Vedral, PRL 58, 5158 (1999)D.E. Browne, M.B. Plenio, and S.F. Huelga, PRL 91, 067901 (2003)

Click

Entangled


Polarising Beamsplitters make Parity Check

PBS

Horizontal Polarization = reflectedVertical Polarization = transmitted

Equally polarized photons emerge on opposite sideOpposite polarized photons emerge on the same side

Parity can be distinguished


Polarization Encoding allows for Parity Measurements

Murao, Plenio, Popescu, Vedral & Knight, 57, R4075 (1998)

CNOT followed by measurement in computational basis is simplya parity check

PBS are sufficient to implement protocol


Many-particle Entanglement

Use atoms to couple todifferent polarizations.

Hyllus, Kieling, Schön, Eisert, Plenio, Scheel, in preparation

Practical Aspects of Quantum Information Imperial College London Martin Plenio Department of Physics...

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