Indecomposable positive maps on positive semidefinite matrices from Mn to Mn+1

Abstract In this paper we obtain a theorem for 2-positive linear maps from Mn(C) to Mn+1(C), where n = 2, 3, 4. In addition, we answer in the affirmative a question that asked if there exists every 2-positive linear map from M3(C) to M4(C) is indecomposable using a family of positive linear maps with Choi matrices of 2-positive maps on positive semidefinite matrices. Further it is shown that 2-positive linear map from M4(C) to M5(C) are indecomposable.