2024/06/05 by Laura Burri, Burri, Laura · 1 citation
Computer Science · #FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Machine Learning and ELM #Neural Networks and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2406.03213
openalex publication_date 2024/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
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∈ (1/2,1), and that the strong converse exponent is determined by the doubly minimized sandwiched Renyi mutual information of order α∈ (1,∞). 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.