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

Prof. Naresh Sharma, Tata Institute of Fundamental Research (TIFR), Mumbai, India

Abstract: We study the fundamental properties of the quantum f-relative entropy, where f(·) is an operator convex function. We give the equality conditions under various properties including monotonicity and joint convexity, and these conditions apply to a class of operator convex functions that we define, and this class is different from the ones previously studied. 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 the Holevo information, the entanglement-assisted capacity, and the coherent information also satisfy the data processing inequality, and give the equality conditions for the f-coherent information.

equality_conditions_for_the_quantum_f-relative_entropy_and_generalized_data_processing_inequalities.txt · Last modified: 2016/09/01 19:15 (external edit)