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

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).