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.
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Communicated by Matthias Christandl.
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The first author was an Andrews Fellow supported by the Department of Mathematics, Purdue University. The third author was supported by a Grant from the Simons Foundation (#527708 to Mark Tomforde)
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Araiza, R., Russell, T. & Tomforde, M. A Universal Representation for Quantum Commuting Correlations. Ann. Henri Poincaré 23, 4489–4520 (2022). https://doi.org/10.1007/s00023-022-01197-7
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DOI: https://doi.org/10.1007/s00023-022-01197-7