Separability Criterion for Bipartite States and Its Generalization to Multipartite Systems

A group of symmetric operators are introduced to carry out the separability criterion for bipartite and multipartite quantum states. All the symmetric operators, represented by a symmetric matrix with only two nonzero elements, and their arbitrary linear combinations are found to be entanglement witnesses. By using these symmetric operators, Wootters' separability criterion for two-qubit states can be generalized to bipartite and multipartite systems in arbitrary dimensions.