The Theory of Quantum Information

John Watrous

doi:10.1017/9781316848142

This largely self-contained book on the theory of quantum information focuses on precise mathematical formulations and proofs of fundamental facts that form the foundation of the subject. It is intended for graduate students and researchers in mathematics, computer science, and theoretical physics seeking to develop a thorough understanding of key results, proof techniques, and methodologies that are relevant to a wide range of research topics within the theory of quantum information and computation. The book is accessible to readers with an understanding of basic mathematics, including linear algebra, mathematical analysis, and probability theory. An introductory chapter summarizes these necessary mathematical prerequisites, and starting from this foundation, the book includes clear and complete proofs of all results it presents. Each subsequent chapter includes challenging exercises intended to help readers to develop their own skills for discovering proofs concerning the theory of quantum information.

‘This is a great book that fulfills a vital need: a unified, precise, and complete presentation of the most important topics in quantum information … Reading the book in detail (verifying the proofs all the while) gave me a solid, confident understanding of the techniques used by those in the field - an understanding that I am eager to apply in the future.’

Stephen A. Fenner Source: SIGACT News

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The Theory of Quantum Information

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-viii

1 - Mathematical Preliminaries
pp 1-57

2 - Basic Notions of Quantum Information
pp 58-123

3 - Similarity and Distance Among States and Channels
pp 124-200

4 - Unital Channels and Majorization
pp 201-249

5 - Quantum Entropy and Source Coding
pp 250-309

6 - Bipartite Entanglement
pp 310-389

7 - Permutation Invariance and Unitarily Invariant Measures
pp 390-463

8 - Quantum Channel Capacities
pp 464-560

References
pp 561-572

Index of Symbols
pp 573-583

Index
pp 584-590

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