On the connection between the theorems of Gleason and of Kochen and Specker

Abstract

We present an elementary proof of a reduced version of Gleason’s theorem and the Kochen–Specker theorem to provide a novel perspective on the relation between both theorems. The proof is based on a set of linear equations for the values of a function, m, on the unit sphere. In the case of Gleason’s theorem, the entire unit sphere needs to be considered, while a finite set of points suffices to prove the Kochen–Specker theorem.