Contextuality and the fundamental theorem of noncommutative algebra

TL;DR

This paper demonstrates that the Kochen-Specker theorem, which addresses contextuality in quantum mechanics, can be derived from Burnside's theorem on noncommutative algebras, linking foundational quantum results to algebraic theorems.

Contribution

It establishes a novel connection showing that quantum contextuality follows from Burnside's fundamental theorem, providing an algebraic foundation for the Kochen-Specker theorem.

Findings

Kochen-Specker theorem derives from Burnside's theorem

Contextuality is inferred from algebraic properties of linear transformations

Provides an algebraic perspective on quantum contextuality

Abstract

In the paper it is shown that the Kochen-Specker theorem follows from Burnside's theorem on noncommutative algebras. Accordingly, contextuality (as an impossibility of assigning binary values to projection operators independently of their contexts) is merely an inference from Burnside's fundamental theorem of the algebra of linear transformations on a Hilbert space of finite dimension.