Doubly minimized sandwiched Renyi mutual information: Properties and operational interpretation from strong converse exponent

Abstract: In this paper, we deepen the study of properties of the doubly minimized sandwiched Renyi mutual information, which is defined as the minimization of the sandwiched divergence of order $\alpha$ of a fixed bipartite state relative to any product state. In particular, we prove a novel duality relation for $\alpha\in [\frac{2}{3},\infty]$ by employing Sion's minimax theorem, and we prove additivity for $\alpha\in [\frac{2}{3},\infty]$. Previously, additivity was only known for $\alpha\in [1,\infty]$, but has been conjectured for $\alpha\in [\frac{1}{2},\infty]$. Furthermore, we show that the doubly minimized sandwiched Renyi mutual information of order $\alpha\in [1,\infty]$ attains operational meaning in the context of binary quantum state discrimination as it is linked to certain strong converse exponents.