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SUMMARY:Quantum generalisations of Kullback–Leibler and Renyi divergence
 s and their application in quantum hypothesis testing - Robert Salzmann
DTSTART:20210428T130000Z
DTEND:20210428T140000Z
UID:TALK158809@talks.cam.ac.uk
CONTACT:Neil Deo
DESCRIPTION:Due to the non-commutativity of quantum mechanics there are in
 finitely many possible quantum generalisations of classical divergences li
 ke the Kullback-Leibler (KL) and Renyi divergences. In this talk I want to
  review how one can decide which of these generalisations is the "right" o
 ne using the context of quantum hypothesis testing.\nFor that I first brie
 fly review the setup of classical binary hypothesis testing and Stein's Le
 mma\, which gives operational meaning to the KL-divergence.\nAfter then re
 calling some quantum basics I talk about the quantum Stein's Lemma and com
 ment on its proof using quantum Renyi divergences. If time permits\, I wil
 l then briefly talk about the Hoeffding and Han-Kobayashi regimes of binar
 y hypothesis testing\, which give operational meaning to the Renyi diverge
 nces\, and comment how the corresponding quantum generalisations give rise
  to the "right" quantum generalisation of the Renyi divergences. 
LOCATION:https://maths-cam-ac-uk.zoom.us/j/95531783868?pwd=U3pPbmYxTXZYRVZ
 MWFBVTkVnWmUvZz09
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