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Let H(1), H(2) be complex Hilbert spaces, H be their Hilbert tensor product and let tr2 be the operator of taking the partial trace of trace class operators in H with respect to the space H(2). The operation tr2 maps states in H (i.e. positive trace class operators in H with trace equal to one) into states in H(1). In this paper we give the full description of mappings that are linear right inverse to tr2. More precisely, we prove that any affine mapping F(W) of the convex set of states in H(1)doi:10.1063/1.1343882 fatcat:i6yvcxdtlbfldlz5sipozflnlq