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

The degree to which a pure quantum state is entangled can be characterized by\nthe distance or angle to the nearest unentangled state. This geometric measure\nof entanglement, already present in a number of settings (see Shimony 1995 and\nBarnum and Linden 2001), is explored for bipartite and multipartite pure and\nmixed states. The measure is determined analytically for arbitrary two-qubit\nmixed states and for generalized Werner and isotropic states, and is also\napplied to certain multipartite mixed states. In particular, a detailed\nanalysis is given for arbitrary mixtures of three-qubit GHZ, W and inverted-W\nstates. Along the way, we point out connections of the geometric measure of\nentanglement with entanglement witnesses and with the Hartree approximation\nmethod.\n