Quantum Entropy and Its Use

This book attempts to provide an overview of quantum entropy theory from the early days of quantum mechanics to recent developments. The mathematical formalism is based on operator theory and functional analysis. The goal is a comprehensive account of the different entropy concepts, their interrelations and use. Examples from 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. The use of quantum entropy quantities is made in perturbation theory, central limit theorems, thermodynamics of spin systems, entropic uncertainty relations, and optical communication.