Quantum Entropy and Its Use

Description

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. Content Level » Research Keywords » Entropie - Entropy Related subjects » Applied & Technical Physics - Quantum Physics - Theoretical and Computational Chemistry Cover Quantum Entropy and Its Use Copyright © Springer-Verlag Berlin Heidelberg 1993 ISBN 3-540-54881-5 ISBN 0-387-54881-5 Preface Contents Introduction Notes and Remarks Part I: Entropies for Finite Quantum Systems 1. Fundamental Concepts Notes and Remarks 2. Postulates for Entropy and Relative Entropy Notes and Remarks 3. Convex Trace Functions Notes and Remarks. Part II: Entropies for General Quantum Systems 4. Modular Theory and Auxiliaries Notes and Remarks 5. Relative Entropy of States of Operator Algebras Notes and Remarks. 6. From Relative Entropy to Entropy Notes and Remarks 7. Functionals of Entropy Type Notes and Remarks Part III: Channeling Transformation and Coarse Graining 8. Channels and Their Transpose Notes and Remarks 9. Sufficient Channels and Measurements Notes and Remarks 10. Dynamical Entropy Notes and Remarks 11. Stationary Processes Notes and Remarks. Part IV: Perturbation Theory 12. Perturbation of States Notes and Remarks 13. Variational Expression of Perturbational Limits Notes and Remarks. Part V: Miscellanea 14. Central Limit and Quasifree Reduction Notes and Remarks. 15. Thermodynamics of Quantum Spin Systems Notes and Remarks. 16. Entropic Uncertainty Relations Notes and Remarks. 17. Temperley-Lieb Algebras and Index Notes and Remarks. 18. Optical Communication Processes Notes and Remarks. Bibliography Subject Index