General Continuity Bounds for Quantum Relative Entropies

• URL: http://arxiv.org/abs/2305.10140v3
• Date: Mon, 5 Feb 2024 14:37:19 GMT
• Title: General Continuity Bounds for Quantum Relative Entropies
• Authors: Andreas Bluhm, \'Angela Capel, Paul Gondolf, Antonio P\'erez-Hern\'andez
• Abstract summary: We introduce a method to prove continuity bounds for 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.
• Score: 0.24999074238880484
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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