In a local hidden-variable description of a Bell experiment, shared hidden data have a distribution independent of the measurement settings. Each outcome depends on the local setting and those shared data, without dependence on the remote setting. Local randomness can be included in the hidden data. Perfect correlations then constrain simultaneous assignments to the possible local measurements. The GHZ theorem shows an all-versus-nothing inconsistency between such assignments and certain three-qubit correlations.
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