Characterizing quantum nonlocality in networks is a challenging problem. This paper proposes using neural networks as numerical tools to determine whether an observed probability distribution can be reproduced using only classical resources. The neural network acts as an oracle, demonstrating that a distribution is classical if it can be learned. The method is applied to several examples in the triangle configuration, providing evidence that a quantum distribution proposed by Gisin is nonlocal and suggesting nonlocality in a new range of parameters for a distribution presented by Renou et al. The method also allows for estimation of noise robustness.

Tamás Kriváchy, Yu Cai, Daniel Cavalcanti, Arash Tavakoli, Nicolas Gisin, Nicolas Brunner