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Wigner's Theorem and geometry of extreme positive maps

We consider transformation maps on the space of states which are symmetries in the sense of Wigner. Due to the convex nature of the space of states, the set of these maps has a convex structure. We investigate the possibility of a complete characterization of extreme maps of this convex body, to be able to contribute to the classification of positive maps. Our study provides a variant of Wigner's theorem originally proved for ray transformations in Hilbert spaces.