Recently, quantum information theory has been developing through a fusion of results from various research fields. This requires that understanding of basic results on diverse topics, and derived from different disciplinary perspectives, is required for appreciating the overall picture. Intended to merge key topics from both the information-theoretic and quantum- mechanical viewpoints, this graduate-level textbook provides a unified viewpoint of quantum information theory and lucid explanations of those basic results, so that the reader fundamentally grasps advances and challenges. For example, advanced topics in quantum communication such as quantum teleportation, superdense coding, quantum state transmission (quantum error-correction), and quantum encryption especially benefit from this unified approach. Unlike earlier treatments, the text requires knowledge of only linear algebra, probability theory, and quantum mechanics, while it treats the topics of quantum hypothesis testingand the discrimination of quantum states, and quantum channel coding (message transmission) with the minimal amount of math needed to convey their essence. Solving the more than 240 exercises provides readers with practice that not only enriches their knowledge of quantum information theory, but also can equip them with the techniques necessary for pursuing their own research in this field.

Autorentext

1990-1994 Faculty of Science, Kyoto Univ.

1994-1996 Master course, Depart of Mathematics, Graduate School of Science,

Kyoto Univ.

1996-1999 Doctor course, Depart of Mathematics, Graduate School of Science,

Kyoto Univ.

1999 March Ph. D. in Mathematics

1998-2000 Research Fellow of the Japan Society for the Promotion of

Science.

2000-2003 Researcher

Lab. for Mathematical Neuroscience (Amari's Lab.),

Brain Science Institute, RIKEN

2003- Head of Research Section

ERATO, Quantum Computation and Information Project,

Japan Science and Technology Agency (JST)

2004- Adjunct Associate Professor

Graduate School of Information Science and Technology

The University of Tokyo

Editorial Bord, International Journal of Quantum Information,

World Scientific (2002-).

Guest Editor, Special Issue of EQIS'03 conference

in International Journal of Quantum Information.

Editor of "Asymptotic Theory of Quantum Statistical Inference: Selected papers" published by World Scientific, 542 pages (2005).

Klappentext

This graduate-level textbook provides a unified viewpoint of quantum information theory that merges key topics from both the information-theoretic and quantum- mechanical viewpoints. The text provides a unified viewpoint of quantum information theory and lucid explanations of those basic results, so that the reader fundamentally grasps advances and challenges. This unified approach makes accessible such advanced topics in quantum communication as quantum teleportation, superdense coding, quantum state transmission (quantum error-correction), and quantum encryption.

Inhalt

Prologue.- Mathematical Formulation of Quantum Systems.- Information Quantities and Parameter Estimation in Classical Systems.- Quantum Hypothesis Testing and Discrimination of Quantum States.- Classical-Quantum Channel Coding (Message Transmission).- State Evolution and Trace-Preserving Completely Positive Maps.- Quantum Information Geometry and Quantum Estimation.- Quantum Measurements and State Reduction.- Entanglement and Locality Restrictions.- Analysis of Quantum Communication Protocols.- Source Coding in Quantum Systems.