Quantum Theory
Sommersemester 2016
Prof. Dr. Michael M. Wolf, Prof. Dr. Robert König
Time & Location: Thursdays, 14.15-15.45, Seminarraum M5 (03.10.011). First meeting on April 14. No meetings on May 26 (holiday) and June 9 (absence).List of topics and suggested references
- Hilbert space, bounded, self-adjoint, unitary and positive operators, spectral theorem, trace, trace class operators. (14.4.)
- Dirac notation, pure and mixed states, purity, density operators, Bloch sphere. (21.4.)
- Measurements: observables, POVMs, Born's rule/postulate, post-measurement states (collapse) and quantum Zeno effect, informationally complete measurements and state tomography. (28.4.)
- Uncertainty relations and joint measurability. (12.5.)
- Tensor products, composite systems, partial trace, Schmidt decomposition, purification. (19.5.)
- Product, separable and entangled states. Entanglement witnesses. LOCC operations, definition of entanglement measures. (2.6.)
- Polytope of classical (local hidden variable) correlations, quantum correlations, classical and quantum values of games, Bell inequalities, Tsirelson bound. (16.6.)
- Unitary and non-unitary dynamics, quantum channels (complete positivity), one-parameter groups and generators, Schrödinger equation. [16] (23.6.)
- Choi-Jamiolkowski isomorphism, Stinespring dilation, Naimark's theorem. (30.6.)
- Teleportation, dense coding, no-cloning, no-signaling, impossible machines. [11,14] (7.7.)
- Fidelity, entropies, Fannes' inequality, strong subadditivity. [2,4,7,12]
- Schumacher compression, Holevo-Schumacher-Westermoreland theorem. [18]
- Quantum capacity, zero-capacity channels, superactivation. [18,13]
Suggested references are as follows: References [5,10,15] give general background material on quantum information/computation. References [1,9,17] cover most of the mathematical concepts necessary for topics 1-9. Additional topic-specific references are given in the list above.
Bibliography
-
- 1
- R. Alicki and M. Fannes, Quantum dynamical systems, Oxford University Press, 2001.
- 2
- K. Audenaert, A Sharp Fannes-type Inequality for the von Neumann Entropy, 2006.
- 3
- M. Fannes, A continuity property of the entropy density for spin lattice systems, Comm. Math. Phys., Vol. 31, No. 4, 291-294 (1973).
- 4
- E. Lieb and M. Ruskai, Proof of the strong subadditivity of quantum-mechanical entropy, J. Math. Phys. 14, 1938 (1973)
- 5
- M. A. Nielsen, I. L. Chuang, Quantum computation and quantum information, Cambridge University Press, 2000.
- 6
- D. Gottesman, An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation, 2009
- 7
- M. Junge, R. Renner, D. Sutter, M. Wilde and A. Winter, Universal recovery from a decrease of quantum relative entropy, 2015
- 8
- R. Horodecki, P. Horodecki, M. Horodecki and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81, 865-942, 2009.
- 9
- M. Keyl, Fundamentals of Quantum Information Theory, Phys. Rep. 369, 431-548, 1999-2015
- 10
- J. Preskill, Quantum Computation, Lecture Notes, 2015.
- 11
- R. F. Werner, All teleportation and dense coding schemes, J. Phys. A: Math. Gen. 34 7081, 2001.
- 12
- M. Ruskai, Another short and elementary proof of strong subadditivity of quantum entropy, Rep. Math. Phys., vol. 60, no. 1, August 2007, Pages 1-12
- 13
- G. Smith, Quantum Channel Capacities, 2010
- 14
- R. F. Werner, Optimal Cloning of Pure States, 1998.
- 15
- R. F. Werner, Quantum Information Theory - an Invitation, 2001.
- 16
- M. Wolf, Quantum Channels and Operations, Lecture Notes, 2012.
- 17
- M. Wolf, Quantum effects, Lecture Notes, 2014.
- 18
- M. Wilde, Quantum Information Theory, Cambridge University Press, 2013.