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We consider transformation maps on the space of states which are symmetriesin the sense of Wigner. Due to the convex nature of the space of states, theset of these maps has a convex structure. We investigate the possibility of acomplete characterization of extreme maps of this convex body, to be able tocontribute to the classification of positive maps. Our study provides a variantof Wigner's theorem originally proved for ray transformations in Hilbertspaces.

Wigner's Theorem and geometry of extreme positive maps