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

TL;DR

This paper establishes that the min-reflected entropy equals the doubly minimized Petz Renyi mutual information of order 1/2 for bipartite quantum states, linking holographic and quantum information measures and resolving open questions.

Contribution

It proves the equivalence of min-reflected entropy and doubly minimized Petz Renyi mutual information of order 1/2, providing new insights into quantum correlation measures.

Findings

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

The equality enables solving previously open questions about these correlation measures.

The work bridges holographic and quantum information theoretical approaches.

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).