Engineering superposition states and tailored probes for nanoresonators via open-loop control.

We show that a nanoresonator can be prepared in mesoscopic superposition states merely by monitoring a qubit coupled to the square of the resonator's 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 nanosystems.