Quantum-informed learning of genuine network nonlocality beyond idealized resources

Abstract

We address the characterization of genuine network nonlocal correlations, which remain highly challenging due to the non-convex nature of local correlations even in the distinct triangle scenario with three sources and three observers implementing one four-outcome measurement. We introduce a scalable causally inferred Bayesian learning framework called the Layered Local Hidden Variable Neural Network (Layered LHV-Net) to learn the local statistics in network Bell tests. Using this framework, we identify a new class of measurement settings that exhibit the most robust nonlocality compared to previously known measurements. Remarkably, our study shows that the nonlocality measure becomes non-zero only when the visibility of the shared Bell state exceeds 0.94, surpassing previously reported noise robustness thresholds. Further, we examine correlations where shared states originate from dissimilar sources, finding that nonlocality is observed only if all the involved states are sufficiently entangled. Finally, we analyze a scenario in which the sources are allowed to share classical randomness. We find that nonlocal correlations persist even when the sources share up to 3 units of randomness, whereas a local model reproducing the quantum correlations only becomes possible when 4 units of shared randomness are available. Apart from the results, the work succeeds in showing that quantum-informed machine learning approaches as foundational frameworks can greatly benefit the field of quantum information.