Geometry of Quantum States: An Introduction to Quantum Entanglement

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Cambridge University Press, Dec 6, 2007 - Science
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Quantum information theory is at the frontiers of physics, mathematics and information science, offering a variety of solutions that are impossible using classical theory. This book provides an introduction to the key concepts used in processing quantum information and reveals that quantum mechanics is a generalisation of classical probability theory. After a gentle introduction to the necessary mathematics the authors describe the geometry of quantum state spaces. Focusing on finite dimensional Hilbert spaces, they discuss the statistical distance measures and entropies used in quantum theory. The final part of the book is devoted to quantum entanglement - a non-intuitive phenomenon discovered by Schrödinger, which has become a key resource for quantum computation. This richly-illustrated book is 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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Outline of quantum mechanics
Coherent states and group actions
The stellar representation
The space of density matrices
Purification of mixed quantum states
Quantum operations
maps versus states
Distinguishability measures
Monotone metrics and measures
Quantum entanglement

Density matrices and entropies

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About the author (2007)

Ingemar Bengtsson is Professor of Physics at Stockholm University. After gaining a Ph.D. in Theoretical Physics from the University of Göteborg (1984), she held post-doctoral positions at CERN, Geneva, and Imperial College, London. She returned to Göteborg in 1988 as a research assistant at Chalmers University of Technnology, before taking up a position as Lecturer in Physics at Stockholm University in 1993. She 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. Her favoured research areas are related to geometry, in the forms of general relativity and quantum mechanics.

Karol Zyckowski is a Professor at the Institute of Physics, Jagiellonian University, Kraków, Poland and also the Center for Theoretical Physics, Polish Academy of Sciences, Warsaw. He gained his Ph.D. (1987) and habilitation (1994) in theoretical physics at Jagiellonian University, and has followed this with a Humboldt Fellowship in Essen, a Fulbright Fellowship at the University of Maryland, College Park and currently a visiting research position at the Perimeter Institute, Waterloo, Ontario. He has been docent at the Academy of Sciences since 1999 and full professor at Jagiellonian University since 2004. Professor Zyczkowski is a member of the Polish Physical Society and the Institute of Physics. He currently serves on the editorial boards of the journals Open Systems and Information Dynamics and Journal of Physics A.

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