Erlangen 2026 – wissenschaftliches Programm
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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 1: Quantum Information: Entropy
MP 1.2: Hauptvortrag
Montag, 16. März 2026, 15:15–15:45, KH 02.013
News on relative entropy — Ricardo Correa da Silva1, •Markus B. Fröb1, Gandalf Lechner1, and Leonardo Sangaletti2 — 1Department Mathematik, FAU Erlangen-Nürnberg, Germany — 2Dipartimento di Fisica, Università di Genova, Italy
I present recent work on a new integral representation for the relative entropy (or Kullback-Leibler divergence) for general von Neumann algebras, generalizing results for matrix algebras. This representation allows easy proofs of its properties such as joint convexity and an extended version of the data processing inequality, namely monotonicity under positive unit-preserving maps. Moreover, it can be used to define Csiszár’s f-divergences for von Neumann algebras, which depend on an arbitrary convex function f, and which give the relative entropy in the special case f(x) = x lnx.
Keywords: Relative entropy; Tomita-Takesaki theory; Csiszár's f-divergences