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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
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