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

TL;DR

This paper offers an elementary proof linking Gleason's and Kochen-Specker's theorems, highlighting their relationship through a simplified approach based on linear equations on the unit sphere.

Contribution

It provides a novel, simplified proof connecting the two theorems, emphasizing their relation via linear equations on the sphere.

Findings

A reduced version of Gleason's theorem is proved using linear equations.

A finite set of points suffices for the Kochen-Specker theorem.

The proof offers a new perspective on the connection between the theorems.

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.