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Permutation-symmetric n qubit pure states can be represented by n points on the surface of the unit sphere by means of the Majorana representation.
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C. D. Cenci, D. W. Lyons, and S. N. Walck arXiv:1011.5229
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It is not known yet to which EF the DC class 𝒟 2 , 1 , 1 \mathcal{D}_{2,1,1} belongs. However, since 𝒟 2 , 1 , 1 \mathcal{D}_{2,1,1} consists of only one SLOCC class, all of its states must belong to a single EF
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P. Ribeiro and R. Mosseri arXiv:1101.2828
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