2025/06/07 by A. S. Holevo, Alexander Semenovich Holevo, A. V. Utkin +3 · 1 citation
Computer Science · Engineering · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Mechanics and Applications #Wireless Communication Security Techniques #cs.IT #math-ph #math.IT #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.2506.06700
openalex publication_date 2025/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Computing accessible information for an ensemble of quantum states is a basic problem in quantum information theory. We show that the recently obtained optimality criterion (A.S. Holevo, Lobachevskii J. Math., 43:7 (2022), 1646-1650), when applied to specific ensembles of states leads to nontrivial tight entropy inequalities that are discrete relatives of the famous log-Sobolev inequality. In this light, the hypothesis of globally information-optimal measurement for an ensemble of equiangular equiprobable states (quantum pyramids) (B.-G. Englert and J. Řeháček, J. Mod. Optics 57 N3 (2010) 218-226) is reconsidered and the corresponding entropy inequalities are proposed. Via the optimality criterion, this suggests also an approach to the proof of the conjectures concerning globally information-optimal observables for quantum pyramids.