Separability of Bipartite Superoperator Based on Witness

Based on the isomorphic relation between operator space L(H) and Hilbert space H^⊕2, Cirac et al. mapped the global superoperator to a mixed state E which has the same separability of the initial superoperator. Zhang et al. Phys. Rev. A 76(2007)012334 provided a calculable lower bound for both the linear and nonlinear witness. We use this bound to detect the entanglement of E to judge the separability of the initial superoperator. With the help of local orthogonal observables, we directly describe the separable condition of superoperator by its each operator. Lastly, using the lower bound of the nonlinear witness, we provide a calculable entanglement factor of bipartite superoperator.