The geometric measure of entanglement for a symmetric pure state with non-negative amplitudes

Abstract

In this paper for a class of symmetric multiparty pure states, we consider a conjecture related to the geometric measure of entanglement: “for a symmetric pure state, the closest product state in terms of the fidelity can be chosen as a symmetric product state.” We show that this conjecture is true for symmetric pure states whose amplitudes are all non-negative in a computational basis. The more general conjecture is still open.