Quantum accessible information and classical entropy inequalities
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914288187211776 |
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| author | Holevo, A. S. Utkin, A. V. |
| author_facet | Holevo, A. S. Utkin, A. V. |
| contents | 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., \textbf{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 \textbf{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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_06700 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum accessible information and classical entropy inequalities Holevo, A. S. Utkin, A. V. Quantum Physics Information Theory Mathematical Physics 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., \textbf{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 \textbf{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. |
| title | Quantum accessible information and classical entropy inequalities |
| topic | Quantum Physics Information Theory Mathematical Physics |
| url | https://arxiv.org/abs/2506.06700 |