Discovering Local Hidden-Variable Models for Arbitrary Multipartite Entangled States and Arbitrary Measurements

Measurement correlations in quantum systems can exhibit non-local behavior, a fundamental aspect of quantum mechanics with applications such as device-independent quantum information processing. However, the explicit construction of local hidden-variable (LHV) models remains an outstanding challenge in the general setting. To address this, we develop an approach that employs gradient-descent algorithms from machine learning to find LHV models which reproduce the statistics of arbitrary measurements for quantum many-body states. In contrast to previous approaches, our method employs a general ansatz, enabling it to discover an LHV model in all cases where the state is local. Therefore, it provides actual estimates for the critical noise levels at which two-qubit Werner states and three-qubit GHZ and W states become non-local. Furthermore, we find evidence suggesting that two-spin subsystems in the ground states of translationally invariant Hamiltonians are local, while bigger subsystems are in general not. Our method now offers a quantitative tool for determining the regimes of non-locality in any given physical context, including scenarios involving non-equilibrium and decoherence.