Minimal Namioka-Phelps tensor product of state spaces equals separable states on the C*-tensor product, with maximal and minimal agreeing precisely when one algebra is commutative.
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Entanglement in C$^*$-algebras: tensor products of state spaces
Minimal Namioka-Phelps tensor product of state spaces equals separable states on the C*-tensor product, with maximal and minimal agreeing precisely when one algebra is commutative.