Detecting Many-Body Bell Nonlocality by Solving Ising Models

Bell non-locality represents the ultimate consequence of quantum entanglement, fundamentally undermining classical tenet that spatially-separated degrees freedom possess objective attributes independently act their measurement. Despite its importance, probing in many-body systems is considered to be a formidable challenge, with computational cost scaling exponentially system size. Here we propose and validate an efficient variational scheme, based on solution inverse Ising problems, which polynomial time can probe whether arbitrary set data compatible local theory; and, if not, it delivers inequality violated by data. We use our approach unveil new inequalities, suitable measurements paradigmatic states (the low-energy Heisenberg antiferromagnets), paving way systematic tests realm.