Controllability of a closed quantum system has been addressed by Tarn and Clark. Their theorem based in control theory states that for a finite-dimensional, closed-quantum system, the system is completely controllable, i.e. an arbitrary unitary transformation of the system can be realized by an appropriate application of the controls if the control operators and the unperturbed Hamiltonian generate the Lie algebra of all Hermitian operators. Complete controllability implies state-to-state controllability.