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The concept of information, as developed by Shannon, is an abstraction where the physical carrier of the
information is not relevant. However, even before the advent of information theory it had become clear that nature
follows the laws of quantum mechanics on small scales. Physicists have found that such physical systems
behave in a fundamentally different way. To understand the fudamental theory of information, we need to study
sources producing quantum states and understand what information means in this context.
Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (25.04.2025)
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JohnWatrous: The Theory of Quantum Information (https://cs.uwaterloo.ca/~watrous/TQI/TQI.pdf)
Michael A. Nielsen, Isaac L. Chuang: Quantum Computation and Quantum Information: 10th Anniversary Edition. Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (25.04.2025)
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• Bit and qubit: quantum states, measurements. • Multiple quantum systems: partial trace, reference systems and purifications, the Schmidt decomposition, entanglement. • Correlations, entanglement and games: Bell games. • Classical and quantum processing: classical channels, quantum channels, CPTP maps and characterization of quantum channels, measurements as quantum channels. • Basic quantum information processing protocols: superdense coding and teleportation, decoupling, recovery and error correction. • Measuring distances and errors: norms of operators, trace distance, fidelity and purified distance, error measures for channels. • Compression: classical compression, quantum compression, asymptotic compression, one-shot information theory and asymptotics. • Entropy: classical and quantum entropy, typical sets and subspaces. • Quantum entropy for multiple parties: entropy inequalities, entropic correlation measures, continuity estimates, proof of weak monotonicity. • Bounds on information processsing: the Holevo bound, bounds for entanglement-assisted communication. • Further optional topics: more about Bell games, quantum state merging, quantum capacity, quantum key distribution. Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (25.04.2025)
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Linear algebra and basics of probability theory are suficient. Knowledge of Quantum Information - NMMB534 will be helpful, but not necessary. No knowledge of physics is required. Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (25.04.2025)
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