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Quantum computation and quantum information. 10th anniversary edition. (English) Zbl 1288.81001
Cambridge: Cambridge University Press (ISBN 978-1-107-00217-3/hbk; 978-0-511-98524-9/ebook). xxxi, 676 p,. (2010).
This is the 10th anniversary edition of one of the earliest textbooks on the title fields and still it is one of the most renowned. The text has not been changed since its first edition in 2000 [reviewed in Zbl 1049.81015].
Besides of 60 pages overview, which contains already quantum teleportation, the Deutsch and Deutsch-Jozsa algorithms, the first part introduces on 50 pages to quantum theory and on another 50 pages to classical computer science. So the book is suitable for experts on the processing of classical data to enter the quantum versions as well as to experts of quantum mechanics to enter the processing of quantum data.
The second part, entitled “Quantum computation”, begins with the circuit model (Section 4). The quantum Fourier Transformation (Section 5) is introduced, its importance is demonstrated in applications in quantum algorithms. Here order finding, factoring (the famous Shor algorithm) as well as period-finding, discrete logarithm, the hidden subgroup problem, and other quantum algorithms are considered. An extra section (Section 6) is devoted to search algorithms, containing the famous Grover algorithm. The final section of part two is concerned with physical realizations of quantum computers. Quantum mechanical, quantum optical, as well as NMR technologies are described.
Part three is entitled “Quantum information” , quantum measurements, quantum operations, channels, quantum noise and stochastics, as well as some properties of quantum state spaces are considered (Sections 8–9). Quantum error correcting methods, quantum codes, stabilizer codes, as well as fault-tolerant computation are topics of Section 10. Shannon and von Neumann entropies are introduced and discussed in Section 11. Applications of quantum entropy are given in Section 12, “Quantum Information theory”, where also quantum cryptography is described.
Six appendices introduce to group theory and group representations, number theory as far as useful in quantum information, as well as some other topics. Many exercises help the reader to become familiar with the stuff presented. Sections close with historical remarks and recommendations to further readings.
Clearly, the book involves only the state of knowledge until the end of the last century which grew up remarkably during ten years research thereafter. But the fundamentals did not change and are well mediated. Mostly one misses a section about entanglement measures and concurrencies for pure and mixed states, but these developments were rather new at the end of the last century. By reasons of didactics the presentation of some topics are spread out over several parts and sections of this book, more cross references would be helpful. Although the text is unchanged since the year 2000 it can still be well recommended as a textbook for beginners.

MSC:
81-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory
81P45 Quantum information, communication, networks (quantum-theoretic aspects)
81P68 Quantum computation
68Q12 Quantum algorithms and complexity in the theory of computing
94A40 Channel models (including quantum) in information and communication theory
94A60 Cryptography
94A17 Measures of information, entropy
94A24 Coding theorems (Shannon theory)
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