The geometric measure of entanglement for a symmetric pure state with positive 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.

Similar results have been obtained independently and with different methods by T-C. Wei and S. Severini, see arXiv:0905.0012v1