Quantum Information 1100-3IK
I. Open quantum systems:
1. Quantum states, operators and observables. Statistical ensembles and density matrices.
2. Qubit and the Bloch representation.
3. Multipartite quantum systems. Reduced density matrix.
4. Evolution of closed and open quantum systems. Stinespring dilation theorem.
5. Quantum channels and decoherence. Choi-Jamiolkowski isomorphism.
6. Quantum 'master' (GKSL) equations and dynamical semigroups.
II. Fundamental aspects of quantum information:
7. General quantum measurements (POVMs). Neumark dilation theorem.
8. Distinguishability of quantum states. Helstrom measurement. Trace distance vs fidelity measures.
9. Entangled states. Schmidt decomposition. Quantum entanglement criteria.
10. Entanglement distillation by LOCC operations. Entanglement measures (distillable, negativity). Bound entangled states.
11. No-cloning theorem and the teleportation of quantum states.
12. Quantum non-locality. Bell inequalities. Hardy's paradox.
13. EPR states and the steerability criteria. Kochen-Specker contextuality.
14. Interpretations of quantum mechanics.
III. Quantum computation:
15. Quantum logical gates and circuits. Universal quantum gate-set.
18. Oracle-based quantum algorithms: Deutsch-Jozsa, Grover.
19. Basics of complexity theory. Quantum Fourier transform and the Shor's algorithm.
20. Quantum error correction.
IV. Quantum communication:
21. Shannon entropy and the mutual information. Shannon's noiseless and the noisy-channel coding theorems (data compression and channel capacity).
22. Von Neumann entropy and quantum mutual information. Schumacher compression and classical capacity of quantum channels (HSW theorem and the Holevo information).
23. Secure key distribution. Secret capacity of a channel and the Csiszar-Korner theorem.
24. Quantum key distribution (QKD). BB84 and E91 protocols. Information reconciliation and privacy amplification procedures. Tolerable QBERs for basic third-party attacks (e.g., intercept&resend).
*25. Thermodynamical aspects of information processing-Landauer's principle.
Main fields of studies for MISMaP
Mode
Prerequisites (description)
Course coordinators
Learning outcomes
Knowledge:
- acquaintance with description of properties and dynamics of composite quantum systems: decoherence phenomenon and quantum channel formalism.
- understanding of fundamental aspects of quantum mechanics and its interpretations: quantum measurement and entanglement, non-classical correlations (phenomena of non-locality, steerability and contextuality).
- familiarity with basics of operation and application of quantum computers: quantum logic gates and circuits, algorithms of Deutch-Jozsa, Grover and Shor.
- understanding of fundamental classical and quantum information theory: data processing, communication and cryptography.
- acquaintance with quantum information protocols: state distinguishability, cloning and teleportation, error correction, compression and coding theorems, cryptographic key distribution.
Skills:
- calculation of quantum state dynamics in quantum channels and probabilities of quantum measurement outcomes.
- verification of quantum state properties such as entanglement or non-locality, and their usefulness for quantum information protocols.
- familiarity with operation and ability to calculate output states in logic circuits of quantum computers.
- ability to evaluate the computational complexity of quantum algorithms and their classical equivalents.
- calculation of the channel capacity for classical and quantum channels in classical data transmission tasks.
- conducting basic security analysis for quantum cryptography protocols.
Assessment criteria
- homework problems
- written exam
Bibliography
1. Alber G., Zeilinger A., et al. Quantum information (STMP 173, Springer, 2001)
2. Nielsen M.A., Chuang I.L. Quantum computation and quantum information (CUP, 2000)
3. Michel Le Bellac, "A short introduction to quantum information and quantum computation" (Cambridge University Press, 2006)
4. Maximilian Schlosshauer, "Decoherence and the quantum-to-classical transition" (Springer, 2007)
5. Gilles van Assche, "Quantum Cryptography and Secret-Key Distillation" (CUP 2006)
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: