Geometric measure of entanglement and applications to bipartite and multipartite quantum states

A geometrically motivated, measure of entanglement, applicable to pure and mixed quantum states involving arbitrary numbers and structures of parties is presented. Such measures are based on the minimal distance between the entangled mixed state and the set of separable mixed states. By contrast, the measure considered is based upon the minimal distance between the entangled pure state and the set of separable pure states, and it is extended to mixed states by a convex-Hull construction.