  We show that a nano-resonator can be prepared in mesoscopic-superposition
states merely by monitoring a qubit coupled to the square of the resonators
position. This works for thermal initial states, and does not require a
third-order nonlinearity. The required coupling can be generated using a simple
open-loop control protocol, obtained with optimal control theory. We simulate
the complete preparation process, including environmental noise. Our results
indicate the power of open-loop control for state-engineering and measurement
in quantum nano-systems.
