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arXiv · 1708.03067

Many-box locality

Yuqian Zhou·Yu Cai·Jean-Daniel Bancal·Fei Gao·Valerio Scarani
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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 $\mathcal{Q}\subset MBL_{\infty}$.

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Yuqian Zhou, Yu Cai, Jean-Daniel Bancal, Fei Gao, Valerio Scarani. 2017-08-10. Many-box locality. https://doi.org/10.1103/physreva.96.052108

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