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