A simplified basis for Bell-Kochen-Specker theorems

摘要

We show that a reduced form of the structural requirements for deterministic hidden variables used in Bell-Kochen-Specker theorems is already sufficient for the no-go results. Those requirements are captured by the following principle: an observable takes a spectral value xif and only if the spectral projector associated with xtakes the value1. We show that the "only if" part of this condition suffices. The proof identifies an important structural feature behind the no-go results; namely, if at leastone projector is assigned the value 1 in any resolution of the identity, then at mostone is.