Computability limits non-local correlations

TL;DR

This paper explores the fundamental limits of non-local correlations, demonstrating that computability constraints impose restrictions beyond the no-signalling principle, even within quantum mechanics.

Contribution

It introduces the idea that computability constraints set additional bounds on non-local correlations beyond no-signalling, applicable to quantum theory.

Findings

Computability limits restrict non-local correlations.

Not all no-signalling correlations are physically realizable.

Quantum mechanics is subject to computability constraints.

Abstract

If the no-signalling principle was the only limit to the strength of non-local correlations, we would expect that any form of no-signalling correlation can indeed be realized. That is, there exists a state and measurements that remote parties can implement to obtain any such correlation. Here, we show that in any theory in which some functions cannot be computed, there must be further limits to non-local correlations than the no-signalling principle alone. We proceed to argue that even in a theory such as quantum mechanics in which non-local correlations are already weaker, the question of computability imposes such limits.