A Universal Representation for Quantum Commuting Correlations

Araiza, Roy; Russell, Travis; Tomforde, Mark

doi:10.48550/arxiv.2102.05827

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Projections In K-aou Spaces1

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2021

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“…is unital and completely positive (Proposition 3.2 of [ART21]). The following theorem shows that π p can be used to characterize when p is a projection in V.…”

Section: Projections In K-aou Spacesmentioning

confidence: 99%

Matricial Archimedean order unit spaces and quantum correlations

Araiza¹,

Russell²,

Tomforde³

2021

Preprint

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We introduce a matricial analogue of an Archimedean order unit space, which we call a k-AOU space. We develop the category of k-AOU spaces and k-positive maps and exhibit functors from this category to the category of operator systems and completely positive maps. We also demonstrate the existence of injective envelopes and C*-envelopes in the category of k-AOU spaces. Finally, we show that finite-dimensional quantum correlations can be characterized in terms of states on finitedimensional k-AOU spaces. Combined with previous work, this yields a reformulation of Tsirelson's conjecture in terms of operator systems and k-AOU spaces.

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“…is unital and completely positive (Proposition 3.2 of [ART21]). The following theorem shows that π p can be used to characterize when p is a projection in V.…”

Section: Projections In K-aou Spacesmentioning

confidence: 99%