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

Rényi reflected entropies of order n ≥ 2 are correlation measures that have been introduced in the field of holography and have since also attracted interest in many-body physics and quantum field theory. In this work, we put the spotlight on the min-reflected entropy, i.e., the Rényi reflected entropy in the limit n → ∞. 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 Rényi 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).