Journal
QUANTUM INFORMATION PROCESSING
Volume 11, Issue 1, Pages 137-160Publisher
SPRINGER
DOI: 10.1007/s11128-011-0238-x
Keywords
Quantum relative entropy; Operator convex functions
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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.
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