Hayashi, Masahito and Markham, Damian and Murao, Mio and Owari, Masaki and Virmani, Shashank (2009) The geometric measure of entanglement for a symmetric pure state with non-negative amplitudes. Journal of Mathematical Physics, 50 (12). p. 122104. ISSN 0022-2488
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.
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