(19) For the model system in Sec. II A, we have N sys = N mol + 1. In Eq. ( ), the αth physical DoF in the system is represented by two independent indices, v α and v ′ α . Accordingly, a single operator O α for the αth DoF is related to a pair of superoperators in twin space, Ôα = O α ⊗ I α and Õα = I α ⊗ O † α , where I α is a unit operator. The whole set of ADOs forms an extended wave function