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, Barnum et al.]. 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. A consequence of our result is that not all of the entropic relations used to derive Tsirelson's bound via information causality in [Pawlowski et al.] are necessary.

5+3 pages, 1 figure. Replaced with version close to that published. Similar results were independently obtained in arXiv:1107.4031

References in corpus (5)

• The uncertainty principle determines the non-locality of quantum mechanics
• A generalized no-broadcasting theorem
• Recovering part of the quantum boundary from information causality
• Macroscopically local correlations can violate information causality
• Implications of Superstrong Nonlocality for Cryptography

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