Doubly minimized Petz and sandwiched Renyi mutual information: Operational interpretation from binary quantum state discrimination
This work provides an operational interpretation for Renyi mutual information in quantum correlation detection, which is incremental as it extends known classical results to quantum systems.
The authors tackled the problem of interpreting doubly minimized Petz and sandwiched Renyi mutual information in quantum information theory by linking them to binary quantum state discrimination, showing that the direct exponent is determined by the Petz version for orders in (1/2,1) and the strong converse exponent by the sandwiched version for orders in (1,∞), generalizing classical results to quantum settings.
The doubly minimized Petz Renyi mutual information of order $α$ is defined as the minimum of the Petz divergence of order $α$ of a given bipartite quantum state relative to all product states. The doubly minimized sandwiched Renyi mutual information is defined analogously, with the Petz divergence replaced by the sandwiched divergence. In this work, we study certain binary quantum state discrimination problems related to correlation detection. We show that the corresponding direct exponent is determined by the doubly minimized Petz Renyi mutual information of order $α\in (1/2,1)$, and that the strong converse exponent is determined by the doubly minimized sandwiched Renyi mutual information of order $α\in (1,\infty)$. This provides an operational interpretation of these types of Renyi mutual information and generalizes previous results for classical probability distributions to the quantum setting. For completeness, we also study the corresponding moderate deviation regime both below and above the threshold, and determine the Stein exponent and the second-order asymptotics.