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Fecha
2023-09-01
Derechos de acceso
info:eu-repo/semantics/openAccess
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IEEE
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Resumen
Based 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.
Descripción
This 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
Este 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
Este 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
Categorías UNESCO
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Citación
Andreas 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
Centro
Escuela Técnica Superior de Ingenieros Industriales
Departamento
Matemática Aplicada I