# 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.

## Key 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.