Joint Distributions and Quantum Nonlocal Models

Abstract

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.

Keywords

• quantum nonlocal models
• testing nonlocal models
• quantum conditional probability
• commutativity
• joint distributions