Finding decompositions of a class of separable states

Abstract We consider the class of separable states which admit a decomposition ∑ i A i ⊗ B i with the B i ’s having independent images. We give a simple intrinsic characterization of this class of states. Given a density matrix in this class, we construct such a decomposition, which can be chosen so that the A i ’s are distinct with unit trace, and then the decomposition is unique. We relate this to the facial structure of the set of separable states. The states investigated include a class that corresponds (under the Choi–Jamiolkowski isomorphism) to the quantum channels called quantum-classical and classical-quantum by Holevo.