Application of the geometric measure of entanglement to three-qubit mixed states

Department of Physics, University of Illinois at Urbana-Champaign,1110 West Green Street, Urbana, Illinois 61801-3080, U.S.A.(Dated: March 26, 2003)The geometric measure of entanglement, originated by Shimony and by Barnum and Linden, isdetermined for a family of tripartite mixed states consisting of aribitrary mixtures of GHZ, W, andinverted-W states. For this family of states, other measures of entanglement, such as entanglementof formation and relative entropy of entanglement, have not been determined. The results forthe geometric measure of entanglement are compared with those for negativity, which are alsodetermined. The results for the geometric measure of entanglement and the negativity provideexamples of the determination of entanglement for nontrivial mixed multipartite states.