The goal of this course is to introduce the concepts and methods of quantum information theory. It starts with an introduction to the mathematical theory of quantum systems and then discusses the basic information-theoretic aspects of quantum mechanics. Further topics include applications such as quantum cryptography and quantum coding theory.
By the end of the course students are able to explain the basic mathematical formalism (e.g. states, channels) and the tools (e.g. entropy, distinguishability) of quantum information theory. They are able to adapt and apply these concepts and methods to analytically solve quantum information-processing problems primarily related to communication and cryptography.
Mathematical formulation of quantum theory: entanglement, density operators, quantum channels and their representations. Basic tools of quantum information theory: distinguishability of states and channels, formulation as semidefinite programs, entropy and its properties. Applications of the concepts and tools: communication of classical or quantum information over noisy channels, quantitative uncertainty relations, randomness generation, entanglement distillation, security of quantum cryptography.
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Nielsen and Chuang, Quantum Information and Computation Preskill, Lecture Notes on Quantum Computation Wilde, Quantum Information Theory Watrous, The Theory of Quantum Information
Performance assessment information (valid until the course unit is held again)