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 wi
tness is further constructed in terms of local orthogonal observables for both bipartite and multipartite systems.
We study the fully entangled fraction of quantum states. An upper bound is obtained for arbitrary dimensional bipartite systems. This bound is shown to be exact for the case of two-qubit systems. An inequality related the fully entangled fraction of
two qubits in a three-qubit mixed state has been also presented.
