A Note on Normal Forms of Quantum States and Separability
  We study the normal form of multipartite density matrices. It is shown that the correlation matrix (CM) separability criterion can be improved from the normal form we obtained under filtering transformations. Based on CM criterion the entanglement witness is further constructed in terms of local orthogonal observables for both bipartite and multipartite systems. 
Ming Li, Shao-Ming Fei and Zhi-Xi Wang