2025/12/11 by Magdalena Musat, Musat, Magdalena, Mikael Rørdam +1
Mathematics · Physics and Astronomy · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Quantum Mechanics and Applications #math.FA #math.OA #quant-ph
paper · pdf · doi:10.48550/arxiv.2512.10410
openalex publication_date 2025/12/11 · openalex created_date 2025/12/13 · openalex updated_date 2026/07/30
We analyze the Namioka-Phelps minimal and maximal tensor products of compact convex sets which arise as the state spaces of unital C^*-algebras. Relatedly, we study entanglement in (infinite dimensional) C^*-algebras. While the minimal Namioka-Phelps tensor product of the state spaces of two C^*-algebras is the well-known set of separable (= un-entangled) states on the (minimal) tensor product of the C^*-algebras, we also describe the more elusive maximal Namioka-Phelps tensor product of state spaces of C^*-algebras. We show that the minimal and maximal tensor products of state spaces of C^*-algebras agree precisely when one of the two C^*-algebras is commutative, which confirms Barker's conjecture in the case where the compact convex sets are state paces of C^*-algebras. Further, the Namioka-Phelps tensor product of the trace simplexes of two or more unital C^*-algebras is shown to be the trace simplex of the (minimal or maximal) tensor product of the C^*-algebras. This enables a systematic way of determining the trace simplex of a tensor product of C^*-algebras.