Geometry of Quantum States:
 
  An Introduction to Quantum Entanglement




 a book by

Ingemar Bengtsson and Karol Życzkowski

second extended edition:  August 2017 by Cambridge University Press









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 Fuchs, University of Massachusetts, Boston  -  see also True Story

 

‘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 Milburn, University of Queensland


Quantum information theory is a branch of science at the frontiers 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 generalised measurements, discrete Wigner functions 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.


contents (2017 edition)


Details:   second edition (August 18, 2017)


* * *


first edition: published May 2006 by Cambridge University Press

      paperback  edition,  Cambridge  January 2008    

(different page numbering: the paperback edition comes in an improved layout
with corrected misprints listed in the erratum below)

Reviews of the first edition by





Details:  Hardback 2006  (ISBN-13: 9780521814515 | ISBN-10: 0521814510)

466 pages, 100 line diagrams,  15 half-tones, 18 tables, 84 exercises

Size 247 x 174 mm, Weight: 1.106 kg
 
                Paperback  2008 (ISBN-13: 9780521891400)

434 pages, 100 line diagrams, 15 half-tones, 18 tables, 84 exercises

Size 247 x 174 mm, Weight: 0.86 kg


Abstract


Quantum information theory is at the frontiers of physics, mathematics and information science, offering a variety of solutions that are impossible using classical theory. The book GEOMETRY OF QUANTUM STATES 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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