Leírás
SZTE, TTIK, Bolyai Intézet, Analízis szeminárium
Abstract. This talk surveys recent developments on quantum $f$-divergences in quantum systems. We discuss three different quantum $f$-divergences of standard, maximal and minimal (or measured) types, as well as Rényi type quantum divergences, first in the finite-dimensional matrix setting and then in the von Neumann algebra setting. Standard $f$-divergences were formerly studied by Petz in a bit more general formula with name quasi-entropy, whose most familiar one is the relative entropy initiated by Umegaki and extended to general von Neumann algebras by Araki. We present basic properties of quantum $f$-divergences and in particular discuss the equality case in their monotonicity inequality under quantum operations. Part of this talk is joint work with Milán Mosonyi.