Year: 2026
Type: article
Abstract: 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, 1646–1650 (2022)), 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 (3), 218–226 (2010)) 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.
Authors: A. S. Holevo, A. V. Utkin
Institution: Steklov Mathematical Institute
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Russian Science Foundation
Award: G3169851932
OpenAlex ID: W4417119709