📝 SummarXiv

Abstract

We address the characterization of genuine network nonlocal correlations, which remains highly challenging due to the non-convex nature of local correlations even in the simplest scenario, and increasingly so when derived from entangled states that deviate from their ideal forms. We introduce a scalable causally-inferred Bayesian learning framework called the LHV layered neural network, which introduces the rank parameter of the non-ideal combined source state as an untapped resource to learn the local statistics in Bell tests. This reveals these correlations to persist close to the Bell states, with a noise robustness of 0.94-0.95 in the triangle scenario, additionally requiring all sources to send only entangled states with joint entangled measurements as resources. Further, we study the robustness of the genuineness to shared randomness in the network scenario. Apart from the results, the work succeeds in showing that machine learning approaches with foundational domain-specific constraints can greatly benefit the field of quantum foundations.