A neural network oracle for quantum nonlocality problems in networks

Abstract: 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.