Closed sets of non-local correlations

TL;DR

This paper introduces the concept of closed sets of correlations to analyze non-local correlations, providing insights into the differences between information-theoretic principles and the limitations of quantum non-locality.

Contribution

It proposes the fundamental notion of closed sets of correlations and explores their implications for understanding quantum non-locality and constraints on physical theories.

Findings

Closed sets of correlations must be closed under natural operations.

Studying closures reveals which principles are fundamentally distinct.

Implications for limits of quantum non-locality and beyond-quantum theories.

Abstract

We introduce a fundamental concept -- closed sets of correlations -- for studying non-local correlations. We argue that sets of correlations corresponding to information-theoretic principles, or more generally to consistent physical theories, must be closed under a natural set of operations. Hence, studying the closure of sets of correlations gives insight into which information-theoretic principles are genuinely different, and which are ultimately equivalent. This concept also has implications for understanding why quantum non-locality is limited, and for finding constraints on physical theories beyond quantum mechanics.