Doubly minimized Petz Renyi mutual information: Properties and operational interpretation from direct exponent

The doubly minimized Petz Renyi mutual information of order α is defined as the minimization of the Petz divergence of order α 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 α∈ [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 α∈ (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.