Many-box locality

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 $MB{L}_N$. 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 $MB{L}_N$ sets are in general not convex. For unbiased marginals, by working in the Fourier space we can prove analytically that $MB{L}_N⊊\mathcal{Q}$ for any finite $N$, while $MB{L}_{\infty }=\mathcal{Q}$. Then, with suitably developed numerical tools, we find an example of a point that belongs to $MB{L}_{16}$ but not to ${\mathcal{Q}}_{1+AB}$. Among the problems that remain open, is whether $\mathcal{Q}\subset MB{L}_{\infty }$.

10 pages, 4 figures, 2 ancillary files; v2: similar to published version

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Cited by in corpus (6)

• Geometry of the set of quantum correlations
• Geometry of the quantum set on no-signaling faces
• Macroscopically nonlocal quantum correlations
• Bipartite nonlocality with a many-body system
• Algebra of Nonlocal Boxes and the Collapse of Communication Complexity
• Bell nonlocality with intensity information only