Quantum accessible information and classical entropy inequalities

• URL: http://arxiv.org/abs/2506.06700v2
• Date: Wed, 09 Jul 2025 14:12:28 GMT
• Title: Quantum accessible information and classical entropy inequalities
• Authors: A. S. Holevo, A. V. Utkin,
• Abstract summary: This paper reconsiders the hypothesis of globally information-optimal measurement for an ensemble of equiangular equiprobable states (quantum pyramids) put forward and numerically substantiated in [2].<n> Via the optimality criterion, this provides also the first proof of the conjecture concerning globally information-optimal observables for quantum pyramids put forward in [2].
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Computing accessible information for an ensemble of quantum states is a basic problem in quantum information theory. The optimality criterion recently obtained in [7], when applied to specific ensembles of states, leads to nontrivial tight lower bounds for the Shannon entropy 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) put forward and numerically substantiated in [2] is reconsidered and the corresponding tight entropy inequalities are proposed and proved. Via the optimality criterion, this provides also the first proof of the conjecture concerning globally information-optimal observables for quantum pyramids put forward in [2].

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