| View Larger Image | Geometry of Quantum States: An Introduction to Quantum Entanglement | Paperbackby Ingemar Bengtsson (Author), Karol Zyczkowski (Author)
| List Price: | $63.00 | | Price: | $56.70 | | You Save: | $6.30 (10%) | | | Available: | Usually ships in 24 hours |
| | Binding: | Paperback | | Publisher: | Cambridge University Press | | Edition: | 1st Edition | | Page Count: | 434 Pages | | Publication Date: | January 14, 2008 | | Sales Rank: | 875,647th |
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EDITORIAL REVIEWS |
Product Description
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. |
CUSTOMER REVIEWS (Average Customer Rating: 2.0 based on 1 review)
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Lower end of the genre by Mayer A. Landau (Rochester, NY)  2 Stars
June 28, 2009
This text applies differential geometry to quantum entanglment. Its exposition falls on the lower end of books of this genre, that is, books that try to introduce advanced mathematics to physics students. The text follows the usual format of replacing proofs with nice pictures and explicit examples and replacing precise mathematical notation with a sloppy one. The problem is that the explicit examples require mathematical structures that the authors avoid explaining. One therefore sees a lot of A=B expressions where the equality, and sometimes the entire equation, is utterly mysterious. For example, equation 3.117 equates translation along the fiber of a principle fiber bundle to the integral over a closed curve in the base manifold of the pullback of an Ehresmann connection 1 form. It is the equation of Ehresmann holonomy. To explain the origin of this equality requires perhaps a chapter of mathematics. Certainly more lines of explanation are required than the number of lines of explanation utilized by the authors, which is zero. Perhaps the authors feel that if they must write down an equation without any prior development, it is best not to draw attention to it. The text is also replete with undefined jargon. For example, they state that the three sphere is parallelizable, but never define the term. Sometimes the jargon is unique to the authors. They still don't define it. The sloppy mathematical notation, of which physicists are so fond, does not help. It tends to confuse the examples. For a math grad student, this text becomes a fun, challenging, and infuriating fill-in workbook. Fun and challenging because some of the unquoted mathematics is not part of the standard math grad student curriculum. Infuriating because you cannot read more than a page or two before you are forced to retrieve a more detailed text for some sort of explanation. For a physics grad student, well... you know you are in trouble if the author's favorite reference is Differential Geometry by Kobayashi and Nomizu (another ridiculous citation is Differential Geometry by Amari, which is, thankfully, out of print). In fact the idea that a physics grad student could read the first seven chapters (the bulk of the mathematical preliminaries) with any real understanding is preposterous. That's unfortunate, because the text does offer a novel and interesting view of quantum states - if only a physics student could read it. For a physics student there is a positive side. Chapter 15 is a good review of bipartite entanglement measures, and the bibliography for bipartite entanglement is the best. But, if you read the book, it should be obvious that the authors have not actually read most of the references they cite.
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