
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 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 models: they are analytically disallowed without the need for experiment, as they imply that all local observables must commute among themselves.
testing nonlocal models, QA1-939, Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects), commutativity, quantum nonlocal models, Quantum measurement theory, state operations, state preparations, quantum conditional probability, joint distributions, Mathematics
testing nonlocal models, QA1-939, Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects), commutativity, quantum nonlocal models, Quantum measurement theory, state operations, state preparations, quantum conditional probability, joint distributions, Mathematics
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