Many-box locality

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 LMBN. We study these sets in the bipartite scenario with two binary measurements, in relation with the sets Q and Q1+AB of quantum and "almost quantum" correlations, respectively. We find that the LMBN sets are, in general, not convex. For unbiased marginals, by working in the Fourier space we can prove analytically that LMBN⊈Q for any finite N, while LMB∞=Q. Then, with suitably developed numerical tools, we find an example of a point that belongs to LMB16 but not to Q1+AB. Among the problems that remain open is whether Q⊂LMB∞.