Coupling capacity in C*-algebras

Given two unital C*-algebras equipped with states and a positive operator in the enveloping von Neumann algebra of their minimal tensor product, we define three parameters that measure the capacity of the operator to align with a coupling of the two given states, and establish a duality formula that shows the equality of two of the parameters. Restricting to abelian C*-algebras we recover instances of Monge-Kantorovich duality and establish a connection with quantitative versions of Arveson\u27s Null Set Theorem. On the other hand, restricting to matrix algebras we recover and generalise quantum versions of Strassen\u27s Theorem. We show that in the latter case our parameters can detect maximal entanglement and separability