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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. 'For years, I have been hoping that somebody would write a book on quantum information theory that was clear, comprehensive, and up to date. This is that book. And the second edition is even better than the first.' Peter Shor, Massachusetts Institute of Technology 'Mark M. Wilde's Quantum Information Theory is a natural expositor's labor of love. Accessible to anyone comfortable with linear algebra and elementary probability theory, Wilde's book brings the reader to the forefront of research in the quantum generalization of Shannon's information theory. What had been a gaping hole in the literature has been replaced by an airy edifice, scalable with the application of reasonable effort and complete with fine vistas of the landscape below. Wilde's book has a permanent place not just on my bookshelf but on my desk.' Patrick Hayden, Stanford University, California Review of previous edition: '... [its] clear, thorough, and above all self-contained presentation will aid quantum information researchers in coming up to speed with the latest results in this area of the field. Meanwhile, the familiar setting and language will help classical information theorists who wish to become more acquainted with the quantum aspects of information processing ... The presentation is well-structured, making it easy to jump to the desired topic and quickly determine on what that topic depends and how it is used going forward ... Quantum Information Theory fills an important gap in the existing literature and will, I expect, help propagate the latest and greatest results in quantum Shannon theory to both quantum and classical researchers.' Joseph M. Renes, Quantum Information Processing Review of previous edition: '... a modern self-contained text ... suitable for graduate-level courses leading up to research level.' Journal of Discrete Mathematical Sciences and Cryptography 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

Quantum Information Theory

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.