A Conjecture on the Amount of Non-Locality

TL;DR

This paper explores the theoretical limits of non-local correlations in quantum physics, proposing a conjecture that links mathematical structures to the Tsirelson bound, which characterizes quantum non-locality.

Contribution

It introduces a conjecture connecting non-local resource bounds with Connes's mathematical results, offering a novel perspective on quantum non-locality constraints.

Findings

Proposes a conjecture relating non-local correlations to mathematical structures.

Suggests a possible motivation for the Tsirelson bound from a new theoretical angle.

Links physical resource bounds to advanced mathematical concepts.

Abstract

Imagine a world in which there exist physical resources for non-local correlations whose CHSH value lies between 2 and $X\leq 4$. Assume that such resources can be mixed in some sense. Using Connes's result on the extension of characteristic 1 semi-rings, we conjecture a possible motivation for quantum mechanical resources obeying the Tsirelson bound $X=2\sqrt{2}$.