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 capacity to align coupling given states. Further, establish duality formula shows equality for operators product relevant C*-algebras. In context abelian C*-algebras, our are related quantitative versions Arveson's null set theorem dualities considered theory optimal transport. On other hand, restricting matrix algebras recover generalize quantum Strassen's theorem. We show latter case can detect maximal entanglement separability.