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SUMMARY:Anna Jencova (Slovakian Academy of Sciences)
DTSTART:20210610T130000Z
DTEND:20210610T134500Z
DTSTAMP:20260423T004515Z
UID:Opalg21/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Opalg21/12/"
 >Renyi relative entropies and noncommutative Lp spaces</a>\nby Anna Jencov
 a (Slovakian Academy of Sciences) as part of Conference on operator algebr
 as and related topics in Istanbul\, 2021\n\n\nAbstract\nThere are several 
 quantum versions of the Renyi relative entropies\, which are fundamental i
 n quantum information theory. Some of these quantities were extended to th
 e general context of normal states of a von Neumann algebra. We concentrat
 e on the class of sandwiched quantum Renyi relative entropies. We show tha
 t this class can be defined in terms of the interpolation Lp spaces due to
  Kosaki. We discuss some properties of these quantities\, especially the c
 onnection to the Araki relative entropy and the data processing inequality
  (monotonicity) with respect to positive unital normal maps. In the second
  part of the talk\, it is shown that reversibility of a 2-positive unital 
 normal map with respect to a set of normal states is characterized by equa
 lity in the data processing inequality.The talk is based on the papers A. 
 Jencova: Renyi relative entropies and noncommutative Lp spaces I and II\, 
 Annales H. Poincare\, 2018 and 2021 (to appear).\n
LOCATION:https://researchseminars.org/talk/Opalg21/12/
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