Ingemar Bengtsson

Geometry of Quantum States (eBook, PDF)

An Introduction to Quantum Entanglement

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 18. August 2017
• Englisch
• ISBN-13: 9781108294690
• Artikelnr.: 49043207

Autorenporträt

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.

Inhaltsangabe

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.