Characterizing quantum nonlocality in networks is a challenging, but
important problem. Using quantum sources one can achieve distributions which
are unattainable classically. A key point in investigations is to decide
whether an observed probability distribution can be reproduced using only
classical resources. This causal inference task is challenging even for simple
networks, both analytically and using standard numerical techniques. We propose
to use neural networks as numerical tools to overcome these challenges, by
learning the classical strategies required to reproduce a distribution. As
such, the neural network acts as an oracle, demonstrating that a behavior is
classical if it can be learned. We apply our method to several examples in the
triangle configuration. After demonstrating that the method is consistent with
previously known results, we give solid evidence that the distribution
presented in [N. Gisin, Entropy 21(3), 325 (2019)] is indeed nonlocal as
conjectured. Finally we examine the genuinely nonlocal distribution presented
in [M.-O. Renou et al., PRL 123, 140401 (2019)], and, guided by the findings of
the neural network, conjecture nonlocality in a new range of parameters in
these distributions. The method allows us to get an estimate on the noise
robustness of all examined distributions.

本研究使用神经网络作为数值工具，通过学习复制分布所需的经典策略，克服了观测概率分布是否仅使用经典资源就可复制的因果推断任务。我们将此方法应用于三角形配置的几个示例，给出了几个分布的噪声稳健性的估计，证明了 [Gisin et al., Entropy 21 (3), 325 (2019)] 中呈现的分布的非局部性猜想，同时提出了 [M.-O. Renou 等人，PRL 123，140401 (2019)] 中相应分布的新参数范围内的非局部性猜想。