Tsirelson's Problem and Asymptotically Commuting Unitary Matrices

TL;DR

This paper explores the relationship between quantum correlations, Tsirelson's problem, and conjectures in operator algebra by examining asymptotically commuting matrices and measures, proposing new formulations and conjectures.

Contribution

It reinterprets Tsirelson's problem in terms of finite-dimensional asymptotically commuting operators and introduces the Stronger Kirchberg Conjecture.

Findings

Reformulation of Tsirelson's problem using asymptotically commuting measures

Introduction of the Stronger Kirchberg Conjecture

Connections between quantum correlations and operator algebra conjectures

Abstract

In this note, we consider quantum correlations of bipartite systems having a slight interaction, and reinterpret Tsirelson's problem (and hence Kirchberg's and Connes's conjectures) in terms of finite-dimensional asymptotically commuting positive operator valued measures. We also consider the systems of asymptotically commuting unitary matrices and formulate the Stronger Kirchberg Conjecture.