2021/09/23 by Roy Araiza, Araiza, Roy, Travis Russell +3
Mathematics · Physics and Astronomy · #46L07 #FOS: Mathematics #Functional Analysis (math.FA) #Homotopy and Cohomology in Algebraic Topology #Mathematical and Theoretical Analysis #Operator Algebras (math.OA) #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.2109.11671
openalex publication_date 2021/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 finite-dimensional k-AOU spaces. Combined with previous work, this yields a reformulation of Tsirelson's conjecture in terms of operator systems and k-AOU spaces.