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arXiv 1708.03067quant-ph
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多盒局部性

Many-box locality

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

备注：
10 pages, 4 figures, 2 ancillary files; v2: similar to published version
发表信息：
Phys. Rev. A 96, 052108 (2017)
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摘要：

人们一直在寻找量子力学的物理或操作定义。已经提出了几个信息原理，这些原理可以由比量子力学限制更少的理论来满足。在这里，我们介绍了“多盒局部性”的原则，这是一个改进的版本，以前提出的“宏观局部性”。这些原则是基于粗粒度的统计数据的几个副本的一个给定的盒子。满足$N$盒的多盒局部性的行为集表示为$MBL_N$。我们研究这些集的二分方案与两个二进制测量，在量子和“几乎量子”的相关性的集合$\mathcal{Q}$和$\mathcal{Q}_{1+AB}$。我们发现，$MBL_N$集一般不是凸的。对于无偏边缘，通过在傅立叶空间中工作，我们可以证明解析地说，$MBL_{N}\subsetneq\mathcal{Q}$对任何有限$N$，而$MBL_{\infty}=\mathcal{Q}$。然后，与适当开发的数值工具，我们找到一个例子的点，属于$MBL_{16}$，但不属于$\mathcal{Q}_{1+AB}$。其中一个问题仍然悬而未决，是是否$\mathcal{Q}\subset MBL_{\infty}$。

英文摘要：

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 $\mathcal{Q}\subset MBL_{\infty}$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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