Many-box locality
Yuqian Zhou, Yu Cai, Jean-Daniel Bancal, Fei Gao, Valerio Scarani

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 boxes is denoted . We study these sets in the bipartite scenario with two binary measurements, in relation with the sets and of quantum and "almost quantum" correlations. We find that the sets are in general not convex. For unbiased marginals, by working in the Fourier space we can prove analytically that for any…
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