Dénes Petz - Böcker

Several applications to quantum information are also included.Introduction to Matrix Analysis and Applications is appropriate for an advanced graduate course on matrix analysis, particularly aimed at studying quantum information.

This monograph, by now a standard reference in the field, provides a complete overview of quantum entropy theory, from the early days of quantum mechanics up to the most recent developments. It employs mathematical formalism based on operator theory and functional analysis with a goal of creating a comprehensive account of the different entropy concepts, their interrelations and use. Among the ideas discussed are entropy of a quantum state, relative entropy, mutual entropy, entropy of a coarse graining and dynamical entropy. Numerous fundamental properties of quantum information measurement are developed, including the von Neumann entropy of a statistical operator and its limiting normalized version, the entropy rate. Use of quantum-entropy quantities is made in perturbation theory, central limit theorems, thermodynamics of spin systems, entropic uncertainty relations, and optical communication. This new softcover corrected reprint contains summaries of recent developments added to the ends of the chapters.

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, it emphasizes concepts and thorough discussions of the fundamental notions and prepares the reader for deeper studies, not least through a selection of well chosen exercises.