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Geometry of Quantum States
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Geometry of Quantum States

Geometry of Quantum States

Ingemar bengtsson (author)|karol Życzkowski (author)

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637 pages, parution le 30/08/2017
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Résumé

Ingemar Bengtsson is a professor of physics at Stockholms Universitet. After gaining a Ph.D. in Theoretical Physics from the Göteborgs universitet (1984), he held post-doctoral positions at CERN, Geneva, and the Imperial College of Science, Technology and Medicine, University of London. He returned to Göteborg in 1988 as a research assistant at Chalmers tekniska högskola, before taking up a position as Lecturer in Physics at Stockholms Universitet in 1993. He was appointed Professor of Physics in 2000. Professor Bengtsson is a member of the Swedish Physical Society and a former board member of its Divisions for Particle Physics and for Gravitation. His research interests are related to geometry, in the forms of classical general relativity and quantum theory.Previous edition: 2007.Preface; 1. Convexity, colours, and statistics; 2. Geometry of probability distributions; 3. Much ado about spheres; 4. Complex projective spaces; 5. Outline of quantum mechanics; 6. Coherent states and group actions; 7. The stellar representation; 8. The space of density matrices; 9. Purification of mixed quantum states; 10. Quantum operations; 11. Duality: maps versus states; 12. Discrete structures in Hilbert space; 13. Density matrices and entropies; 14. Distinguishability measures; 15. Monotone metrics and measures; 16. Quantum entanglement; 17. Multipartite entanglement; Appendix 1. Basic notions of differential geometry; Appendix 2. Basic notions of group theory; Appendix 3. Geometry - do it yourself; Appendix 4. Hints and answers to the exercises; Bibliography; Index.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.Second editionIllustrationsQC174.12Quantum theory.|Information theory.1EnglandCambridgeIngemar Bengtsson and Karol Zyczkowski.Advance praise: '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

Advance praise: '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

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Éditeur(s) Cambridge University Press
Auteur(s) Ingemar bengtsson (author)|karol Życzkowski (author)
Parution 30/08/2017
Nb. de pages 637
Format 174 x 247
Poids 1578g
EAN13 9781107026254

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