Quantum Information Theory

Introduces many concepts and mathematical tools in quantum information theory, with over 100 pages of new material and exercises.

Mark M. Wilde (Author)

9781107176164, Cambridge University Press

Hardback, published 6 February 2017

776 pages, 80 b/w illus. 3 tables 300 exercises
25.8 x 17.8 x 4.6 cm, 1.45 kg

Review of previous edition: '… the book does a phenomenal job of introducing, developing and nurturing a mathematical sense of quantum information processing … In a nutshell, this is an essential reference for students and researchers who work in the area or are trying to understand what it is that quantum information theorists study. Wilde, as mentioned in his book, beautifully illustrates 'the ultimate capability of noisy physical systems, governed by the laws of quantum mechanics, to preserve information and correlations' through this book. I would strongly recommend it to anyone who plans to continue working in the field of quantum information.' Subhayan Roy Moulick, SIGCAT News

Developing many of the major, exciting, pre- and post-millennium developments from the ground up, this book is an ideal entry point for graduate students into quantum information theory. Significant attention is given to quantum mechanics for quantum information theory, and careful studies of the important protocols of teleportation, superdense coding, and entanglement distribution are presented. In this new edition, readers can expect to find over 100 pages of new material, including detailed discussions of Bell's theorem, the CHSH game, Tsirelson's theorem, the axiomatic approach to quantum channels, the definition of the diamond norm and its interpretation, and a proof of the Choi–Kraus theorem. Discussion of the importance of the quantum dynamic capacity formula has been completely revised, and many new exercises and references have been added. This new edition will be welcomed by the upcoming generation of quantum information theorists and the already established community of classical information theorists.

Preface to the second edition
Preface to the first edition
How to use this book
Part I. Introduction: 1. Concepts in quantum Shannon theory
2. Classical Shannon theory
Part II. The Quantum Theory: 3. The noiseless quantum theory
4. The noisy quantum theory
5. The purified quantum theory
Part III. Unit Quantum Protocols: 6. Three unit quantum protocols
7. Coherent protocols
8. Unit resource capacity region
Part IV. Tools of Quantum Shannon Theory: 9. Distance measures
10. Classical information and entropy
11. Quantum information and entropy
12. Quantum entropy inequalities and recoverability
13. The information of quantum channels
14. Classical typicality
15. Quantum typicality
16. The packing lemma
17. The covering lemma
Part V. Noiseless Quantum Shannon Theory: 18. Schumacher compression
19. Entanglement manipulation
Part VI. Noisy Quantum Shannon Theory: 20. Classical communication
21. Entanglement-assisted classical communication
22. Coherent communication with noisy resources
23. Private classical communication
24. Quantum communication
25. Trading resources for communication
26. Summary and outlook
Appendix A. Supplementary results
Appendix B. Unique linear extension of a quantum physical evolution
References
Index.

Subject Areas: Signal processing [UYS], Quantum physics [quantum mechanics & quantum field theory PHQ], Coding theory & cryptology [GPJ], Information theory [GPF]