Geometry of Quantum States

An Introduction to Quantum Entanglement

Karol Zyczkowski author Ingemar Bengtsson author

Format:Hardback

Publisher:Cambridge University Press

Published:18th Aug '17

Currently unavailable, and unfortunately no date known when it will be back

This hardback is available in another edition too:

Geometry of Quantum States cover

This new edition describes the space of quantum states and the theory of quantum entanglement from a geometric perspective.

The second edition of a book that has become a standard reference for researchers working on geometric aspects of quantum entanglement and quantum theory of information. Its comprehensive style makes it suitable for students of physics, information science, and mathematics wishing to learn more about quantum mechanics and quantum entanglement.Quantum information theory is a branch of science at the frontier of physics, mathematics, and information science, and offers a variety of solutions that are impossible using classical theory. This book provides a detailed introduction to the key concepts used in processing quantum information and reveals that quantum mechanics is a generalisation of classical probability theory. The second edition contains new sections and entirely new chapters: the hot topic of multipartite entanglement; in-depth discussion of the discrete structures in finite dimensional Hilbert space, including unitary operator bases, mutually unbiased bases, symmetric informationally complete generalized measurements, discrete Wigner function, and unitary designs; the Gleason and Kochen–Specker theorems; the proof of the Lieb conjecture; the measure concentration phenomenon; and the Hastings' non-additivity theorem. This richly-illustrated book will be useful to a broad audience of graduates and researchers interested in quantum information theory. Exercises follow each chapter, with hints and answers supplied.

'True story:  A few years ago my daughter took a break from her usual question, 'Dad, what is your favourite colour?' and asked instead, 'What is your favourite shape?' I was floored! 'What a wonderful question; my favourite shape is Hilbert space!' 'What does it look like?' she asked. My answer: 'I don't know! But every day when I go to work, that's what I think about.' What I was speaking of, of course, is the geometry of quantum-state space. It is as much a mystery today as it was those years ago, and maybe more so as we learn to focus on its most key and mysterious features. This book, the worn first-edition of which I've had on my shelf for 11 years, is the indispensable companion for anyone's journey into that exotic terrain. Beyond all else, I am thrilled about the inclusion of two new chapters in the new edition, one of which I believe goes to the very heart of the meaning of quantum theory.' Christopher A. Fuchs, University of Massachusetts, Boston
'The quantum world is full of surprises as is the mathematical theory that describes it. Bengtsson and Życzkowski prove to be expert guides to the deep mathematical structure that underpins quantum information science. Key concepts such as multipartite entanglement and quantum contextuality are discussed with extraordinary clarity. A particular feature of this new edition is the treatment of SIC generalised measurements and the curious bridge they make between quantum physics and number theory.' Gerard J. Milburn, University of Queensland
Praise for the first edition: 'Geometry of Quantum States can be considered an indispensable item on a bookshelf of everyone interest in quantum information theory and its mathematical background.' Miłosz Michalski, editor of Open Systems and Information Dynamics
Praise for the first edition: 'Bengtsson's and Zyczkowski's book is an artful presentation of the geometry that lies behind quantum theory … the authors collect, and artfully explain, many important results scattered throughout the literature on mathematical physics. The careful explication of statistical distinguishability metrics (Fubini-Study and Bures) is the best I have read.' Gerard Milburn, University of Queensland

ISBN: 9781107026254

Dimensions: 254mm x 182mm x 30mm

Weight: 1390g

632 pages

2nd Revised edition