Anna Jencova: Renyi relative entropies and noncommutative Lp spaces

Speaker : Anna Jencova, Slovakian Academy of Sciences.
Day 3, Session 1 of the Operator Algebras in Istanbul 2021 Conference
Abstract : There are several quantum versions of the Renyi relative entropies, which are fundamental in quantum information theory. Some of these quantities were extended to the general context of normal states of a von Neumann algebra. We concentrate on the class of sandwiched quantum Renyi relative entropies. We show that this class can be defined in terms of the interpolation Lp spaces due to Kosaki. We discuss some properties of these quantities, especially the connection 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 equality 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).

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