Quantum Information Theory

1.  Introduction and Motivation

2. Classical Information
    Shannon Entropy and data compression.
    Conditional entropy and mutual entropy, Venn diagrams
    Channel capacity
    Physical aspects of information.

3. Quantum Information
    Preliminaries A:  composite systems, tensor products.
    Some new features: No cloning theorem, dense coding.    
    Preliminaries B:  quantum ensembles and the density matrix.
    The von-Neumann entropy.
    Quantum data compression
    Distinguishability of quantum states.
    Generalized measurements (POVMs).

4. Entanglement.

        Foundations:
        The EPR paradox.
        Bell's inequalities.
        "Super correlations";  Popescu Rohrlich Box.  *

        Uses of entanglement:
         Teleportation.
         Dense Coding.
         Remote operations and "non-local" measurements.*
         Improved accuracy and speedup of measurements.

         Quantifying Entanglement:
         Schmidt decomposition.
         Changes under LOCC.
         Concentration and dilution.
         Reversibility.
         Entanglement of mixed states.
         Distillation and bound entanglement. *
         Multi-party Entanglement.*
 

(*לא בחומר למבחן )
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5. Quantum Computation.
     Complete set of gates.
     Quantum  simulations.
     Correcting errors

6.  Quantum Cryptography.
      Secrete key.
      Privacy amplification.

7. Quantum information processing (QIP).
    Introduction:  interaction of light and matter.
    Generation of entangled photons.  
    The ion-trap quantum computer.
    Entanglement manipulations in a Bose Einstein condensates.
    QIP using condensed matter systems.

8. New models for QIP:
    Teleportation as a resource for computing.
    Computation with identical particles. (linear optics)
    Measurement based schemes using cluster states. (optical lattices).
    Adiabatic computers.

9. Entanglement in continues systems.
    Gaussian entanglement.
    Entanglement in harmonic and spin chain systems.
    Entanglement and quantum phase transitions.

Bibliography

"Quantum computation and quantum information",  Nielsen and Chuang 2000.
"Elements of  information theory" (the classical), Cover and Thomas.
Richard Feynman,  "Lectures on Computations".
Asher Peres, "Quantum theory concepts and methods". (ch. 5, 6, 9)

J. Preskill's  Lecture notes on quantum computations.
My Lecture notes  Quantum Information given during 2003

Research papers can be found at the quant-ph archive, or  Google Scholar


Einstein, Podolsky, Rosen Phys. Rev. 47, 777 (1935)
J. F. Clauser, M. A. Horne, A. Shimony and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969)
The first experimental test that Bell's inq. are violated, A. Aspect, J. Dalibard and G. Roger, Phys. Rev. Lett. 49, 1804 (1982)
Dense coding, C. H. Bennett and S. J. Wiesner, Phys. Rev. Lett. 69, 2881 (1992)
Teleportation, C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993) 
EPR pairs in quantum cryptography, A. K. Ekert, Phys. Rev. Lett. 67, 661
Improvement of Frequency Standards with Quantum Entanglement , S. F. Huelga et.al, Phys. Rev. Lett. 79, 3865 - 3868 (1997)
Teleportation is a computation primitive: Daniel Gottesman, Isaac L. Chuang, Nature 402, 390-393 (1999)

Concentrating partial entanglement by local operations, Bennett et. al,  Physical Review A, 53.2046 ,1996.
Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels, Phys. Rev. Lett. 76, 722 - 725 (1996)
Quantum information can be negative, M. Horodecki, J. Oppenheim, A. Winter, Nature 436:673-676 (2005)

Assignments

Ex 1.
Ex 2.
Ex 3.
Ex 4.
Ex. 5.
Ex. 6

החומר למבחן כולל את  פרקים 1-4

Exam

Reception time:  Thursday's 17-18.