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.
Quantum Information Processing – Springer Journals
Published: Mar 18, 2011
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