Min-reflected entropy = doubly minimized Petz Renyi mutual information of order 1/2

Laura Burri

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arXiv · 2502.18433

Min-reflected entropy = doubly minimized Petz Renyi mutual information of order 1/2

Laura Burri

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Abstract

Renyi reflected entropies of order $n \geq 2$ are correlation measures that have been introduced in the field of holography. In this work, we put the spotlight on the min-reflected entropy, i.e., the Renyi reflected entropy in the limit $n \rightarrow \infty$. We show that, for general bipartite quantum states, this measure is identical to another measure originating from the field of quantum information theory: the doubly minimized Petz Renyi mutual information of order $1/2$. Furthermore, we demonstrate how this equality enables us to answer several previously open questions, each concerning one of the two correlation measures (or generalizations of them).

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Laura Burri. 2025-02-25. Min-reflected entropy = doubly minimized Petz Renyi mutual information of order 1/2. https://arxiv.org/abs/2502.18433

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