New Invariants and Separability criterion of the Mixed States: Bipartite Case

Hao Chen

Published 2001-07-23, updated 2001-08-12Version 2

We introduce algebraic sets in the complex projective spaces for the mixed states in bipartite quantum systems as their invariants under local unitary operations. The algebraic sets of the mixed state have to be the union of the linear subspaces if the mixed state is separable. Some examples are given and studied based on our criterion