Many-box locality

TL;DR

This paper introduces the principle of many-box locality, a refined version of macroscopic locality, and studies its relation to quantum and almost quantum correlations, revealing that finite many-box locality sets are strictly smaller than quantum sets.

Contribution

It defines and analyzes the many-box locality principle, showing its properties and relation to quantum correlations, including analytical and numerical results.

Findings

MBL_N sets are generally non-convex.

MBL_N is a subset of quantum correlations for finite N.

An example of a point in MBL_16 not in almost quantum correlations was found.

Abstract

There is an ongoing search for a physical or operational definition for quantum mechanics. Several informational principles have been proposed which are satisfied by a theory less restrictive than quantum mechanics. Here, we introduce the principle of "many-box locality", which is a refined version of the previously proposed "macroscopic locality". These principles are based on coarse-graining the statistics of several copies of a given box. The set of behaviors satisfying many-box locality for $N$ boxes is denoted $MBL_N$. We study these sets in the bipartite scenario with two binary measurements, in relation with the sets $\mathcal{Q}$ and $\mathcal{Q}_{1+AB}$ of quantum and "almost quantum" correlations. We find that the $MBL_N$ sets are in general not convex. For unbiased marginals, by working in the Fourier space we can prove analytically that $MBL_{N}\subsetneq\mathcal{Q}$ for any finite $N$, while $MBL_{\infty}=\mathcal{Q}$. Then, with suitably developed numerical tools, we find an example of a point that belongs to $MBL_{16}$ but not to $\mathcal{Q}_{1+AB}$. Among the problems that remain open, is whether $\mathcal{Q}\subset MBL_{\infty}$.