Tsirelson's problem and purely atomic von Neumann algebras

TL;DR

This paper demonstrates that bipartite behaviors with a purely atomic von Neumann algebra representation are inherently non-relativistic, linking algebraic properties to physical constraints.

Contribution

It establishes a connection between purely atomic von Neumann algebras and the non-relativistic nature of bipartite behaviors, providing new insights into algebraic quantum models.

Findings

Purely atomic von Neumann algebras imply non-relativistic behavior.

Field representations with atomic algebras restrict relativistic models.

The result clarifies the algebraic structure underlying quantum non-locality.

Abstract

It is shown that if a bipartite behavior admits a field representation in which Alice (or Bob's) observable algebra generates a purely atomic von Neumann algebra then it is non-relativistic.