  We consider a non-resonant system of finitely many bilinear Schroedinger
equations with discrete spectrum driven by the same scalar control. We prove
that this system can approximately track any given system of trajectories of
density matrices, up to the phase of the coordinates. The result is valid both
for bounded and unbounded Schroedinger operators. The method used relies on
finite-dimensional control techniques applied to Lie groups. We provide also an
example showing that no approximate tracking of both modulus and phase is
possible
