A Simplified Basis for Bell-Kochen-Specker Theorems

TL;DR

This paper simplifies the foundational assumptions behind Bell-Kochen-Specker theorems, showing that a weaker condition still leads to the same no-go results in quantum hidden variable theories.

Contribution

It demonstrates that the 'if and only if' condition can be reduced to only the 'if' part, streamlining the structural requirements for these theorems.

Findings

Reduced the structural assumptions needed for Bell-Kochen-Specker theorems.

Proved that assigning a projector the value 1 implies at most one such projector in any resolution.

Identified a key structural feature underlying the no-go results.

Abstract

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 x if and only if the spectral projector associated with x takes the value 1. 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 least one projector is assigned the value 1 in any resolution of the identity, then at most one is.