Geometrical Structure of Entangled States and the Secant Variety.

We investigate the geometrical structure of entangled and separable bipartite and multipartite states based on the secant variety of the Segre variety. We show that the Segre variety coincides with the space of separable multipartite state and the higher secant variety of the Segre variety coincides with the space of entangled multipartite states. [ABSTRACT FROM AUTHOR]