在更小维度中利用量子相关性超越一比特通信
Beating one bit of communication with quantum correlations in smaller dimensions
AI总结：
本文构造了迄今维度最小、模拟需超过一比特通信的量子相关性示例，并通过将最大1比特得分转化为输入二分优化问题完成证明。
摘要：
作为 Bell 定理的一个结果，对某些纠缠态进行测量所得的统计规律，无法仅用局部隐变量来模拟。必须提供的通信量是非经典性的一个直观量化指标。尽管一般而言这一通信量显然可能非常大，但令人惊讶的是，要找到模拟时需要超过一比特通信的简单量子相关性示例一直十分困难。本文报告了迄今为止最简单的示例，它存在于 $(5,2,5,5)$ Bell 场景中［此前已知的最小情形存在于 $(7,3,16,16)$ 场景中］。该证明建立在如下观察之上：寻找最大的 1 比特得分等价于寻找输入的一种二分划分，使两个子游戏的局部得分之和在该划分下达到最大。
英文摘要：
As a consequence of Bell's theorem, the statistics of measurements on some entangled states cannot be simulated with local hidden variables alone. The amount of communication that must be supplied is an intuitive quantifier of nonclassicality. While it is obvious that this amount can be very large in general, it has been surprisingly difficult to find simple examples of quantum correlations, whose simulation requires more than one bit of communication. In this paper, we report the simplest example to date, which lives in the $(5,2,5,5)$ Bell scenario [the previously known smallest case living in the $(7,3,16,16)$ scenario]. The proof is built on the observation that finding the largest 1-bit score is equivalent to finding the bipartition of the inputs, in which the sum of the local scores of the two subgames is maximal.
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