Tsirelson's bound from a generalised data processing inequality

Abstract

The strength of quantum correlations is bounded from above by Tsirelson's bound. We establish a connection between this bound and the fact that correlations between two systems cannot increase under local operations, a property known as the data processing inequality. More specifically, we consider arbitrary convex probabilistic theories. These can be equipped with an entropy measure that naturally generalizes the von Neumann entropy, as shown recently in [Short and Wehner]. We prove that if the data processing inequality holds with respect to this generalized entropy measure then the underlying theory necessarily respects Tsirelson's bound. We moreover generalise this statement to any entropy measure satisfying certain minimal requirements.