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Following an idea of Choi, we obtain a decomposition theorem for k-positivelinear maps from Mm to Mn, where 2<=k<min{m,n}. As a consequence, we give anaffirmative answer to Kye's conjecture (also solved independently by Choi) thatevery 2-positive linear map from M3 to M3 is decomposable.

All 2-positive linear maps from M3 to M3 are decomposable