Quantum Information Theory: Mathematical Foundation

Description

This graduate textbook provides a unified view of quantum information theory. Clearly explaining the necessary mathematical basis, it merges key topics from both information-theoretic and quantum- mechanical viewpoints and provides  lucid explanations of the basic results. Thanks to this unified approach, it makes accessible such advanced topics in quantum communication as quantum teleportation, superdense coding, quantum state transmission (quantum error-correction) and quantum encryption. Since the publication of the preceding book Quantum Information: An Introduction, there have been tremendous strides in the field of quantum information. In particular, the following topics – all of which are addressed here – made seen major advances: quantum state discrimination, quantum channel capacity, bipartite and multipartite entanglement, security analysis on quantum communication, reverse Shannon theorem and uncertainty relation. With regard to the analysis of quantum security, the present book employs an improved method for the evaluation of leaked information and identifies a remarkable relation between quantum security and quantum coherence. Taken together, these two improvements allow a better analysis of quantum state transmission. In addition, various types of the newly discovered uncertainty relation are explained. Presenting a wealth of new developments, the book introduces readers to the latest advances and challenges in quantum information. To aid in understanding, each chapter is accompanied by a set of exercises and solutions. Front Matter....Pages i-xli Mathematical Formulation of Quantum Systems....Pages 1-24 Information Quantities and Parameter Estimation in Classical Systems....Pages 25-94 Quantum Hypothesis Testing and Discrimination of Quantum States....Pages 95-153 Classical-Quantum Channel Coding (Message Transmission)....Pages 155-195 State Evolution and Trace-Preserving Completely Positive Maps....Pages 197-251 Quantum Information Geometry and Quantum Estimation....Pages 253-322 Quantum Measurements and State Reduction....Pages 323-356 Entanglement and Locality Restrictions....Pages 357-490 Analysis of Quantum Communication Protocols....Pages 491-568 Source Coding in Quantum Systems....Pages 569-605 Back Matter....Pages 607-636