The Theory of Quantum Information

Formal development of the mathematical theory of quantum information with clear proofs and exercises. For graduate students and researchers.

John Watrous (Author)

9781107180567, Cambridge University Press

Hardback, published 26 April 2018

598 pages, 9 b/w illus. 40 exercises
25.5 x 17.9 x 3.7 cm, 1.2 kg

'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, SIGACT News

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.

1. Mathematical preliminaries
2. Basic notions of quantum information
3. Similarity and distance among states and channels
4. Unital channels and majorization
5. Quantum entropy and source coding
6. Bipartite entanglement
7. Permutation invariance and unitarily invariant measures
8. Quantum channel capacities
References
List of symbols and notations
Index.

Subject Areas: Signal processing [UYS], Mathematical theory of computation [UYA], Quantum physics [quantum mechanics & quantum field theory PHQ], Algebraic geometry [PBMW], Algebra [PBF], Discrete mathematics [PBD], Coding theory & cryptology [GPJ], Information theory [GPF]