Equality conditions of Data Processing Inequality for $\alpha$-$z$ R\'enyi relative entropies
Mathematical Physics
2020-11-02 v2 Functional Analysis
math.MP
Quantum Physics
Abstract
The - R\'enyi relative entropies are a two-parameter family of R\'enyi relative entropies that are quantum generalizations of the classical -R\'enyi relative entropies. In \cite{zhang20CFL} we decided the full range of for which the Data Processing Inequality (DPI) is valid. In this paper we give algebraic conditions for the equality in DPI. For the full range of parameters , we give necessary conditions and sufficient conditions. For most parameters we give equivalent conditions. This generalizes and strengthens the results of Leditzky, Rouz{\'e} and Datta in \cite{LRD17DPI}.
Keywords
Cite
@article{arxiv.2007.06644,
title = {Equality conditions of Data Processing Inequality for $\alpha$-$z$ R\'enyi relative entropies},
author = {Haonan Zhang},
journal= {arXiv preprint arXiv:2007.06644},
year = {2020}
}
Comments
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