Joint Distributions and Quantum Nonlocal Models

A standard result in quantum mechanics is this: if two observables are commuting then they have a classical joint distribution in every state.A converse is demonstrated here: If a Metal Wallet Card classical joint distribution for the pair agrees with standard quantum facts, then the observables must commute.This has consequences for some historical and recent quantum nonlocal 2 Layers Wood Sign models: they are analytically disallowed without the need for experiment, as they imply that all local observables must commute among themselves.