Equality conditions for the quantum f-relative entropy and generalized data processing inequalities

Equality conditions for the quantum f-relative entropy and generalized data processing inequalities We consider the quantum f-relative entropy where f is an operator convex function. We define a family of operator convex functions and for that family, we give the equality conditions for the quantum f-relative entropy under various properties including monotonicity and joint convexity. The quantum f-entropy is defined in terms of the quantum f-relative entropy and we study its properties giving the equality conditions in some cases. We then show that the f-generalizations of some well-known information theoretic quantities also satisfy the data processing inequality and give equality conditions for the f-coherent information for the family of functions that we define. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Equality conditions for the quantum f-relative entropy and generalized data processing inequalities

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Publisher
Springer Journals
Copyright
Copyright © 2011 by Springer Science+Business Media, LLC
Subject
Physics; Computer Science, general; Theoretical, Mathematical and Computational Physics; Quantum Physics; Mathematics, general; Physics, general
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-011-0238-x
Publisher site
See Article on Publisher Site

Abstract

We consider the quantum f-relative entropy where f is an operator convex function. We define a family of operator convex functions and for that family, we give the equality conditions for the quantum f-relative entropy under various properties including monotonicity and joint convexity. The quantum f-entropy is defined in terms of the quantum f-relative entropy and we study its properties giving the equality conditions in some cases. We then show that the f-generalizations of some well-known information theoretic quantities also satisfy the data processing inequality and give equality conditions for the f-coherent information for the family of functions that we define.

Journal

Quantum Information ProcessingSpringer Journals

Published: Mar 18, 2011

References

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