Geometry of Quantum States: An Introduction to Quantum Entanglement

Przednia okładka
Cambridge University Press, 18 sie 2017
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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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Spis treści

Convexity colours and statistics
1
Geometry of probability distributions
29
Much ado about spheres
63
Complex projective spaces
103
Outline of quantum mechanics
138
Coherent states and group actions
165
The stellar representation
191
The space of density matrices
219
maps versus states
296
Discrete structures in Hilbert space
313
Density matrices and entropies
355
Distinguishability measures
386
Monotone metrics and measures
402
Quantum entanglement
433
Multipartite entanglement
493
Epilogue
544

Purification of mixed quantum states
249
Quantum operations
267
do it yourself
553
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Informacje o autorze (2017)

Ingemar Bengtsson is a professor of physics at Stockholms Universitet. After gaining a Ph.D. in Theoretical Physics from the Gteborgs 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 Gteborg in 1988 as a research assistant at Chalmers tekniska hgskola, 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.

Karol yczkowski is a professor at the Institute of Physics, Uniwersytet Jagiellonski, Krakw, Poland, and also at the Center for Theoretical Physics, Polska Akademia Nauk, Warsaw. He gained his Ph.D. and habilitation in theoretical physics at Uniwersytet Jagiellonski, and has followed this with a Humboldt Fellowship in Essen, a Fulbright Fellowship at the University of Maryland, College Park, and a visiting research position at the Perimeter Institute for Theoretical Physics, Ontario. He has been docent at the Academy of Sciences since 1999 and full professor at Uniwersytet Jagiellonski since 2004. Professor yczkowski is a member of the Polish Physical Society and Academia Europaea. He works on quantum information, dynamical systems and chaos, quantum and statistical physics, applied mathematics, and theory of voting.

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