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

• URL: http://arxiv.org/abs/2406.01699v1
• Date: Mon, 3 Jun 2024 18:01:00 GMT
• Title: Doubly minimized Petz Renyi mutual information: Properties and operational interpretation from direct exponent
• Abstract summary: The doubly minimized Petz Renyi mutual information of order $alphain (1/2,1)$ is defined as the minimization of the Petz divergence of order $alpha$ of a fixed bipartite quantum state. 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 $alphain (1/2,1)$.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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