Abstract

There is a plethora of different entropic quantities in quantum information theory which are interesting both from the mathematical and operational points of view. It is hence desirable to have a unifying mathematical framework for the study of these different quantities. We provide such a framework by defining a two-parameter family of relative Renyi entropies which acts as a parent quantity for all known entropies. In particular, the quantum relative entropy, the recently defined quantum Renyi divergences, as well as the original quantum relative Renyi entropies can be obtained from them. Consequently, the data-processing inequality, which is an essential property for these quantities, follows directly from the data-processing inequality for this new family. Interestingly, the latter can be proved by taking a detour into complex analysis, as will be elucidated in the talk.This work has been done jointly with Koenraad Audenaert.



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