Separability is an important problem in theory of quantum entanglement. By using the Bloch representation of quantum states in terms of the Heisenberg-Weyl observable basis, we present a new separability criterion for bipartite quantum systems. It is shown that this criterion can be better than the previous ones in detecting entanglement. The results are generalized to multipartite quantum states.
We study the equivalence of mixed states under local unitary transformations in bipartite system and three partite system. First we express quantum states in Bloch representation. Then based on the coefficient matrices, some invariants are constructed in terms of the products, trace and determinant of matrices. This method and results can be extended to multipartite high dimensional system.
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