A Universal Representation for Quantum Commuting Correlations

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.