The doubly minimized Petz Renyi mutual information of order $\alpha$ is defined as the minimization of the Petz divergence of order $\alpha$ of a fixed bipartite quantum state relative to any product state. In this work, we establish several properties of this type of Renyi mutual information, including its additivity for $\alpha\in [1/2,2]$. As an application, we show that the direct exponent of certain binary quantum state discrimination problems is determined by the doubly minimized Petz Renyi mutual information of order $\alpha\in (1/2,1)$. This provides an operational interpretation of this type of Renyi mutual information, and generalizes a previous result for classical probability distributions to the quantum setting.

翻译：双重最小化Petz Rényi $\alpha$阶互信息定义为固定二分量子态相对于任意乘积态的Petz $\alpha$阶散度的最小化。本工作中，我们建立了此类Rényi互信息的若干性质，包括其在$\alpha\in [1/2,2]$范围内的可加性。作为应用，我们证明特定二元量子态判别问题的直接指数由$\alpha\in (1/2,1)$阶双重最小化Petz Rényi互信息决定。这为此类Rényi互信息提供了操作解释，并将经典概率分布的已有结果推广至量子情形。