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–

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.

**Hardcover:**632 pages

**ISBN-13:**978-1107026254**ISBN-10:**1107026253**Product Dimensions:**6.8 x 1.2 x 9.7 inches**; Shipping Weight:**3.2 pounds

* * *

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

- P. Slater
published
by MathSciNet as MR2230995 (2007k:81001) in September 2007

- D.W. Hook published in J. Phys A 41, 019001 (2008)
- M. Michalski published in Open Systems & Information Dynamics 15, 91-92 (2008)
- G. Milburn published in Quantum Information and Computation 8, 0860 (2008)

- contents (2006 edition)

- bibliography 2006

- erratum (concerning the
**2006 hardback**edition only) - erratum II (concerning the
**2008 paperback**edition only)

Size 247 x 174 mm, Weight:
1.106 kg

Paperback 2008 (ISBN-13: 9780521891400)

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.

Back to home page of Karol
Zyczkowski
Last update: November 26, 2017