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Open Quantum Systems Decoherence Quantum Entropy Information Measures Entanglement Theory Quantum Correlations

Equality conditions of Data Processing Inequality for α-z Rényi relative entropies

arXiv

Authors: Haonan Zhang

Year

2020

Paper ID

22261

Status

Preprint

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~2 min

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Abstract

The α-z Rényi relative entropies are a two-parameter family of Rényi relative entropies that are quantum generalizations of the classical α-Rényi relative entropies. In \cite{zhang20CFL} we decided the full range of (α,z) 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 (α,z), we give necessary conditions and sufficient conditions. For most parameters we give equivalent conditions. This generalizes and strengthens the results of Leditzky, Rouz{é} and Datta in \cite{LRD17DPI}.

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The α-z Rényi relative entropies are a two-parameter family of Rényi relative entropies that are quantum generalizations of the classical α-Rényi relative entropies.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2007.06644 [2] arXiv https://arxiv.org/abs/2007.06644 [3] Publisher https://arxiv.org/abs/2007.06644

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