This concise and readable book addresses primarily readers with a background in classical statistical physics and introduces quantum mechanical notions as required. Conceived as a primer to bridge the gap between statistical physics and quantum information, a field to which the author has contributed significantly himself, it emphasizes concepts and thorough discussions of the fundamental notions and prepares the reader for deeper studies, not the least through a selection of well chosen exercises.

Focuses on the real introductory explanation of certain important concepts of quantum information theory and quantum statistics The mathematically rigorous presentation is supported by numerous examples and exercises With an appendix summarizing the relevant part of linear analysis The author is well known for his ability in carefully and thoroughly presenting this subject matter at the interface of two major fields of research

Autorentext

Fumio Hiai is an Emeritus Professor at the Graduate School of Information Science, Tohoku University, Sendai, Japan, whose research interests are operator theory, operator algebras and quantum probability. He published more than 95 papers and several books on various subjects of mathematics, including more than 20 papers on matrix analysis. His recent interest is also quantum information.

Klappentext

Based on lectures given by the author, this book focuses on providing reliable introductory explanations of key concepts of quantum information theory and quantum statistics - rather than on results. The mathematically rigorous presentation is supported by numerous examples and exercises and by an appendix summarizing the relevant aspects of linear analysis. Assuming that the reader is familiar with the content of standard undergraduate courses in quantum mechanics, probability theory, linear algebra and functional analysis, the book addresses graduate students of mathematics and physics as well as theoretical and mathematical physicists. Conceived as a primer to bridge the gap between statistical physics and quantum information, a field to which the author has contributed significantly himself, it emphasizes concepts and thorough discussions of the fundamental notions to prepare the reader for deeper studies, not least through the selection of well chosen exercises.

Inhalt
Prerequisites from Quantum Mechanics.- Information and its Measures.- Entanglement.- More About Information Quantities.- Quantum Compression.- Channels and Their Capacity.- Hypothesis Testing.- Coarse-grainings.- State Estimation.- Appendix: Auxiliary Linear and Convex Analysis.