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Continuity of Quantum Entropic Quantities via Almost Convexity

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dc.contributor.authorBluhm, Andreas
dc.contributor.authorCapel, Angela
dc.contributor.authorGondolf, Paul
dc.contributor.authorPérez Hernández, Antonio
dc.contributor.funderAgencia Estatal de Investigación
dc.contributor.funderComunidad de Madrid
dc.date.accessioned2026-02-20T12:22:03Z
dc.date.available2026-02-20T12:22:03Z
dc.date.issued2023-09-01
dc.descriptionThis is the Accepted Manuscript of an article published by IEEE in "IEEE Transactions on Information Theory, 69, 2023" , available online: https://doi.org/10.1109/TIT.2023.3277892
dc.descriptionEste es el manuscrito aceptado de un artículo publicado por IEEE en "IEEE Transactions on Information Theory, 69, 2023" , disponible en línea: https://doi.org/10.1109/TIT.2023.3277892
dc.description.abstractBased on the proofs of the continuity of the conditional entropy by Alicki, Fannes, and Winter, we introduce in this work the almost locally affine (ALAFF) method. This method allows us to prove a great variety of continuity bounds for the derived entropic quantities. First, we apply the ALAFF method to the Umegaki relative entropy. This way, we recover known almost tight bounds, but also some new continuity bounds for the relative entropy. Subsequently, we apply our method to the Belavkin-Staszewski relative entropy (BS-entropy). This yields novel explicit bounds in particular for the BS-conditional entropy, the BS-mutual and BS-conditional mutual information. On the way, we prove almost concavity for the Umegaki relative entropy and the BS-entropy, which might be of independent interest. We conclude by showing some applications of these continuity bounds in various contexts within quantum information theory.en
dc.description.provenanceMade available in DSpace on 2026-02-20T12:22:03Z (GMT). No. of bitstreams: 1 Perez_Hernandez_Antonio_Continuity_Entropic_Q_ANTONIO PEREZ HERNAN.pdf: 2789403 bytes, checksum: 80849acfa2390f376bcbf63e5efd3614 (MD5) Previous issue date: 2023-09-01en
dc.description.versionversión final
dc.identifier.citationAndreas Bluhm, Ángela Capel, Paul Gondolf, Antonio Pérez-Hernández (2023). Continuity of Quantum Entropic Quantities via Almost Convexity. IEEE Transactions on Information Theory, 69(9), 5869-5901. URL: https://doi.org/10.1109/TIT.2023.3277892. ISSN: 0018-9448 eISSN: 1557-9654
dc.identifier.doihttps://doi.org/10.1109/TIT.2023.3277892
dc.identifier.eissn1557-9654
dc.identifier.issn0018-9448
dc.identifier.urihttps://hdl.handle.net/20.500.14468/31875
dc.journal.issue9
dc.journal.titleIEEE Transactions on Information Theory
dc.journal.volume69
dc.language.isoen
dc.page.final5901
dc.page.initial5869
dc.publisherIEEE
dc.relation.centerEscuela Técnica Superior de Ingenieros Industriales
dc.relation.departmentMatemática Aplicada I
dc.relation.projectidinfo:eu-repo/grantAgreement/S2018/TCS-4342/QUITEMAD-CM
dc.relation.projectidinfo:eu-repo/grantAgreement/MICIN/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-113523GB-I00/Análisis Matemático y Teoría de la Información Cuántica
dc.relation.projectidinfo:eu-repo/grantAgreement/UE/ERC/GAPS (N. 648913)/Spectral gaps in interacting quantum systems
dc.relation.projectidinfo:eu-repo/grantAgreement/DFG/CRC 2023-2026/ID 470903074 – TRR 352/Mathematics of Many-Body Quantum Systems and Their Collective Phenomena
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
dc.subject12 Matemáticas
dc.titleContinuity of Quantum Entropic Quantities via Almost Convexityen
dc.typeartículoes
dc.typejournal articleen
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relation.isAuthorOfPublication5df1117e-e057-404a-a139-4d4aab6e5298
relation.isAuthorOfPublication.latestForDiscovery5df1117e-e057-404a-a139-4d4aab6e5298
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