Two-outcome synchronous correlation sets and Connes' embedding problem

TL;DR

This paper links Connes' embedding problem to the weak Tsirelson problem via two-outcome synchronous correlation sets, showing their extreme points relate to universal C*-algebras and confirming the Tsirelson problems in three-experiment cases.

Contribution

It establishes an equivalence between Connes' embedding problem and the weak Tsirelson problem for two-outcome synchronous sets and analyzes these sets using universal C*-algebras.

Findings

Connes' embedding problem is equivalent to the weak Tsirelson problem in this setting.

Extreme points of the correlation sets can be realized with universal C*-algebras.

The strong and weak Tsirelson problems are affirmed in the three-experiment case.

Abstract

We show that Connes' embedding problem is equivalent to the weak Tsirelson problem in the setting of two-outcome synchronous correlation sets. We further show that the extreme points of two-outcome synchronous correlation sets can be realized using a certain class of universal C*-algebras. We examine these algebras in the three-experiment case and verify that the strong and weak Tsirelson problems have affirmative answers in that setting.