A note on the geometric interpretation of Bell's inequalities

TL;DR

This paper offers an elementary geometric interpretation of Bell's inequalities for three spins, showing they define the tetrahedron of all spin correlation matrices as an intersection of half-spaces.

Contribution

It provides a direct and elementary geometric proof linking Bell's inequalities to the structure of spin correlation matrices.

Findings

Bell's inequalities characterize the tetrahedron of correlation matrices.

The geometric interpretation clarifies the role of Bell's inequalities in quantum correlations.

The approach simplifies understanding of the correlation space for three spins.

Abstract

Using results of Pitowsky and Gupta, we show in a direct, elementary fashion that, in the case of three spins, Bell's inequalities indeed provide a representation of the tetrahedron of all spin correlation matrices as intersection of half-spaces.