  We discuss how to prepare an Ising chain in a GHZ state using a single global
control field only. This model does not require the spins to be individually
addressable and is applicable to quantum systems such as cold atoms in optical
lattices, some liquid- or solid-state NMR experiments, and many nano-scale
quantum structures. We show that GHZ states can always be reached
asymptotically from certain easy-to-prepare initial states using adiabatic
passage, and under certain conditions finite-time reachability can be ensured.
To provide a reference useful for future experimental implementations three
different control strategies to achieve the objective, adiabatic passage,
Lyapunov control and optimal control are compared, and their advantages and
disadvantages discussed, in particular in the presence of realistic
imperfections such as imperfect initial state preparation, system inhomogeneity
and dephasing.
