  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) into the states in H that is right
inverse to tr2 is given by the tensor product of W with some state D in H(2).
In addition we investigate a representation of the quantum mechanical state
space by probability measures on the set of pure states and a representation --
used in the theory of stochastic Schroedinger equations -- by probability
measures on the Hilbert space. We prove that there are no affine mappings from
the state space of quantum mechanics into these spaces of probability measures.
