  We show that we can achieve global density-operator controllability for most
N-dimensional bilinear Hamiltonian control systems with general fixed couplings
using a single, locally-acting actuator that modulates one energy-level
transition. Controllability depends upon the position of the actuator and
relies on the absence of either decompositions into non-interacting subgroups
or symmetries restricting the dynamics to a subgroup of SU(N). These results
are applied to spin-chain systems and used to explicitly construct control
sequences for a single binary-valued switch actuator.
