Thermalization and Unruh Radiation for a Uniformly Accelerated Charged Particle
Dominique Unruh 3 September 2012 Quantum Cryptography Dominique Unruh.
-
Upload
blaze-kristopher-garrett -
Category
Documents
-
view
228 -
download
1
Transcript of Dominique Unruh 3 September 2012 Quantum Cryptography Dominique Unruh.
Dominique Unruh 3 September 2012
Quantum Cryptography
Dominique Unruh
Dominique Unruh 2
Organization
• Lecture: Tuesday 10.15am• Practice: Wednesday 10.15am– Problem solving as a group
• (sometimes switched)
• Homework: Due after approx. one week• 50% needed for exam
Dominique Unruh 3
Organizatorial
• Black board lecture (except today)• Material:– Board photos– Lecture notes (short)– Book: Nielsen, Chuang, “Quantum Computation
and Quantum Information” (not required)
• Deregistering: Not after deadline
Dominique Unruh 4
Scope of the lecture
• No physics (almost)– Do you need electrodynamics to understand
Turing-machines?– Mathematical abstraction of quantum
computation/communication• Intro to Quantum
computation/communication• Selected topics in quantum crypto
Dominique Unruh 5
Requirements
• No physics needed• Some crypto background recommended– (To have a context / the big picture)
• Some linear algebra will be used– You should not be afraid of math– Can do recap during tutorial ask!!!
Dominique Unruh
Organizatorial
• Questions?
Dominique Unruh 7
Quantum Mechanics
Dominique Unruh Quantum Cryptography 8
Double Slit Experiment
• Light falls through two slits (S2)
• Light-dark pattern occurs
• Reason: Light is a wave → Interference
Dominique Unruh Quantum Cryptography 9
Double Slit Experiment
• Send a single photon at a time• Photon either goes through left or right
path• After a while, interference pattern occurs• Each photon “interferes with itself”
→ Physicists puzzled• Solution: Quantum mechanics:– Photon takes both ways in superposition
Dominique Unruh 10Quantum Cryptography
Superposition
• If two situations are possible, nature “does not always decide”– Both situations happen “in superposition”– (Doesn’t need to make sense now)
• Only when we look, “nature decides”
• Schrödinger’s cat
Dominique Unruh 11Quantum Cryptography
Quantum Mechanics
• Superposition: Several things happen “at once”
• Our intuition is classical, we cannot understand this
• Mathematical notions allow to handle QM, even if we do not understand it
Dominique Unruh 12
Quantum Computing
Dominique Unruh 13
Church-Turing Thesis
• Turing: Definition of Turing-machines• Church-Turing thesis:
→ Turing-Machine characterises physical computability
Usually: Efficient = polynomial-time
Any physically computable function can be computed by a Turing machine
efficiently
efficient
Strong
Dominique Unruh 14
Randomized algorithms
• 1970s: Solovay-Strassen primality test• No deterministic test known (at that time)• Polynomial identity:
No deterministic test today
Any efficiently physically computable function can be computed by an efficient
Turing machine
probabilistic
Dominique Unruh 15
Enters: The Quantum Computer
• Strong Church-Turing extended once– Perhaps has to be extended again
• Feynman 1982:– Simulating quantum systems difficult for TMs– Quantum system can simulate quantum system
• Probabilistic Church-Turing thesis wrong?– Unknown so far… But seems so…
Dominique Unruh 16
Quantum Algorithms
• Deutsch-Jozsa 1992:– Testing whether function is balanced or constant– No practical relevance– Shows: Quantum Computers more powerful than
classical• Shor 1994:– Factorization of integers
• Grover 1996:– Quadratic speed-up of brute-force search
Dominique Unruh 17
Today
• No quantum computers(except for toy models)
• Cannot execute quantum algorithms• Future will tell
Dominique Unruh 18
Quantum Cryptography
Dominique Unruh 19
Quantum Key Exchange
• Bennet, Brassard 1984:– Key exchange using quantum communication
• Idea:– Measurement destroys state→ Adversary cannot eavesdrop unnoticed
Dominique Unruh 20
Quantum Key ExchangeAlice Bob
Polarisation:
Measures
Sends basis
Shared key bits
Dominique Unruh 21
Quantum Key Exchange – AttackAlice Bob
Polarisation:
measuresAdversary measures→ Bit destroyed→ Alice+Bob: different keys→ Attack detected
Changed by measurement
Caution: This is only the intuition.Security analysis much more involved.
(Took 12 additional years…)
Dominique Unruh 22
Quantum Key Exchange
• Idea proposed 1984• First security proof: Mayers 1996• Possible with today’s technology– Single photon sources– Polarisation filters
• No complexity assumptions– Impossible classically
• Details later in lecture
Dominique Unruh 23
Quantum Cryptography
• Any cryptography using quantum– Key exchange– Bit commitment– Oblivious transfer– Zero knowledge– Signatures
• Often: Quantum Crypto = Key Exchange– Other applications often ignored
Dominique Unruh 24
End of Intro