A Universal Representation for Quantum Commuting Correlations

TL;DR

This paper constructs a mathematical framework linking quantum commuting correlations to order unit spaces, providing a new way to analyze quantum correlations using operator system techniques.

Contribution

It introduces a novel construction of an Archimedean order unit space whose state space matches quantum commuting correlations, using fundamental order and operator system methods.

Findings

Explicit construction of the order unit space for quantum correlations

Characterization of positive contractions as projections on Hilbert space

Bridging quantum correlations with operator system theory

Abstract

We explicitly construct an Archimedean order unit space whose state space is affinely isomorphic to the set of quantum commuting correlations. Our construction only requires fundamental techniques from the theory of order unit spaces and operator systems. Our main results are achieved by characterizing when a finite set of positive contractions in an Archimedean order unit space can be realized as a set of projections on a Hilbert space.