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arXiv · 2305.10140

General Continuity Bounds for Quantum Relative Entropies

Andreas Bluhm·Ángela Capel·Paul Gondolf·Antonio Pérez-Hernández
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Abstract

In this article, we generalize a proof technique by Alicki, Fannes and Winter and introduce a method to prove continuity bounds for entropic quantities derived from different quantum relative entropies. For the Umegaki relative entropy, we mostly recover known almost optimal bounds, whereas, for the Belavkin-Staszewski relative entropy, our bounds are new. Finally, we use these continuity bounds to derive a new entropic uncertainty relation.

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Andreas Bluhm, Ángela Capel, Paul Gondolf, Antonio Pérez-Hernández. 2023-05-17. General Continuity Bounds for Quantum Relative Entropies. https://doi.org/10.1109/isit54713.2023.10206734

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