Appears in collection : Operator Algebras and Quantum Information Theory

In this talk, we use the duality between n-partite separable states and positive multi-linear maps with n-1 variables, to give a necessary criterion for three qubit separability in terms of diagonal and anti-diagonal entries. If all the entries are zero except for diagonal and anti-diagonal entries, then our characterization is also sufficient for separability. Many important classes of three qubit states like Greenberger-Horne-Zeilinger diagonal states are in this class. We give the characterization in terms of a norm in the four dimensional complex spaces. We also exhibit examples of non-decomposable positive bi-linear maps which generate exposed rays in the cone of all positive bi-linear maps in 2x2 matrices. The exposedness enables us to detect three qubit PPT entanglement of nonzero volume.