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. Density matrices and entropies; 13. Distinguishability measures; 14. Monotone metrics and measures; 15. Quantum entanglement; Epilogue; Appendices; References; Index.
An introduction to key concepts of quantum information processing for graduates and researchers.
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.
'Geometry of Quantum States, not being a quantum mechanics textbook
by itself, provides an extensive and detailed insight behind the
scenes of entanglement and, as such, can serve as a very useful
supplementary text for quantum mechanics courses. Written in a very
lucid and engaging style, with numerous illustrations … The
spectrum of potential readers … is by no means limited to students
and newcomers. It is comprehensive enough to serve as a valuable
reference for all researchers interested in quantum information
theory. Geometry of Quantum States can be considered an
indispensable item on a bookshelf of everyone interest in quantum
information theory and its mathematical background.' Milosz
Michalski, Open Systems and Information Dynamics
'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
'Bengtsson and Zyczkowski's beautifully illustrated volume …
attempts to cover considerable ground in its 418 pages.' D. W.
Hook, Journal of Physics
'The authors, distinguished mathematical physicists, have written a
markedly distinctive, dedicatedly pedagogical, suitably rigorous
text, designed, in part, for advanced undergraduates familiar with
the principles of quantum mechanics. The book, pleasing in
character and enthusiastic in tone, has many stimulating diagrams
and tables, as well as problem sets (with hints and answers
supplied at the end). The diverse topics covered - conveniently all
assembled here - reflect the geometrically-oriented, fundamental
quantum-information-theoretic interests and expertise of the two
authors.' Paul B. Slater, Mathematical Reviews
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