General Continuity Bounds for Quantum Relative Entropies

Andreas Bluhm (1) , Ángela Capel (2) , Paul Gondolf (2) , Antonio Pérez-Hernández (3)

1 CAPP - Calculs algorithmes programmes et preuves
2 Mathematisches Institut [Tübingen]
3 UNED - Universidad Nacional de Educación a Distancia

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. This is a short version of [1].

Domains: Quantum Physics [quant-ph]

Andreas Bluhm, Ángela Capel, Paul Gondolf, Antonio Pérez-Hernández. General Continuity Bounds for Quantum Relative Entropies. 2023 IEEE International Symposium on Information Theory (ISIT), Jun 2023, Taipei, Taiwan. pp.162-167, ⟨10.1109/ISIT54713.2023.10206734⟩. ⟨hal-04438904⟩