A general theorem on local parts of hidden variable models

TL;DR

This paper generalizes a recent result to higher-dimensional bipartite systems, proving that hidden variable theories cannot have local parts, meaning their local averages must match quantum mechanics, regardless of the system's dimension.

Contribution

It extends the no-local-part result from two-dimensional systems to any finite-dimensional maximally entangled bipartite state.

Findings

Hidden variable models cannot have local parts in higher dimensions

Local averages in hidden variable theories match quantum predictions

The result applies to all finite-dimensional maximally entangled states

Abstract

We extend to any maximally entangled state of a bipartite system whose constituents are arbitrarily (but finite) dimensional the result, recently derived for two-dimensional constituents, that hidden variable theories cannot have local parts, i.e., that their local averages cannot differ from the quantum mechanical ones.