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

• URL: http://arxiv.org/abs/2406.03213v2
• Date: Thu, 20 Feb 2025 08:32:55 GMT
• Title: Doubly minimized sandwiched Renyi mutual information: Properties and operational interpretation from strong converse exponent
• Abstract summary: We prove a novel duality relation for $alphain [frac23,infty]$ by employing Sion's minimax theorem.<n>We show that the doubly minimized sandwiched Renyi mutual information of order $alphain [1,infty]$ attains operational meaning in the context of binary quantum state discrimination.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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