equality_conditions_for_the_quantum_f-relative_entropy_and_generalized_data_processing_inequalities

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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)