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Quantum information. An introduction to basic theoretical concepts and experiments. (English) Zbl 0974.81005

Springer Tracts in Modern Physics. 173. Berlin: Springer. xi, 216 p. (2001).
This book is a well organized collection of articles by experts in the field of quantum information theory. The articles deal with theoretical, mathematical and computer science aspects of quantum information. All these aspects are dealt with on an introductory level thus making the book useful even for a reader just entering into the field of quantum information processing.
The first chapter by Alber provides an interesting overview of the quantum information theory. The second chapter by Werner introduces the basic concepts of quantum information theory and describes the fundamental mathematical structures underlying recent and current developments. Examples of possible and impossible quantum processes are discussed in detail in this chapter. In the third chapter the first experimental realizations of basic quantum schemes based on entangled quantum pairs are discussed. These experiments on entanglement-based quantum cryptography, dense coding and quantum teleportation demonstrate the important role photons play in current experiments.
The basic theoretical concepts of quantum computation and the mathematical structure underlying quantum algorithms are discussed in chapter 4 by Beth and Rotteler. In particular, it is demonstrated how results in the theory of signal processing can be used for the development of new fast quantum algorithms. A short introduction to the theory of quantum error correction is also presented.
A comprehensive account of the mathematical structure of entanglement and of the significance of mixed entangled states for quantum information processing is presented in chapter 5 by M. Horodecki, P. Horodecki and R. Horodecki. This section gives a state-of-the art presentation of bound entanglement and its implication for processing quantum information.

MSC:

81P68 Quantum computation
94A15 Information theory (general)
81-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory
68Q05 Models of computation (Turing machines, etc.) (MSC2010)
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