Separability Criteria For Arbitrary Quantum Systems

The purpose of this paper is to obtain a sufficient and necessary condition as a criteria to test whether an arbitrary multipartite state is entangled or not. Based on the tensor expression of a multipartite pure state, the paper shows that a state is separable iff $| \mathbf{C}(\rho)| $ =0 for pure states and iff $C(\rho)$ vanishes for mixed states.