Jencova: [WS2] Quantum Rényi divergences on von Neumann algebras and reversibility of (completely) positive unital maps

Speaker
Anna Jencova, Slovak Academy of Sciences

Abstract
Reversibility, or sufficiency, of a quantum channel with respect to a set of states was introduced by Petz, who obtained several equivalent conditions characterizing this property. A notable characterization is by equality in the data processing inequality (DPI) of the relative entropy. This result was subsequently extended to a number of other quantities satisfying the DPI, in particular to the class of alpha-z-Rényi divergences. In the original work of Petz, as well as in subsequent works, the channels were assumed to be completely positive, or at least 2-positive. As it turned out, the DPI for the Rényi divergences still holds if the channels are only required to be positive. In this talk, we review the theory of Petz sufficient channels and the Rényi divergences in the setting of von Neumann algebras, discussing some results that remain true if the channel is only assumed to be positive.