  The cavity-optomechanical radiation pressure interaction provides the means
to create entanglement between a mechanical oscillator and an electromagnetic
field interacting with it. Here we show how we can utilize this entanglement
within the framework of time-continuous quantum control, in order to engineer
the quantum state of the mechanical system. Specifically, we analyze how to
prepare a low-entropy mechanical state by (measurement-based) feedback cooling
operated in the blue detuned regime, the creation of bipartite mechanical
entanglement via time-continuous entanglement swapping, and preparation of a
squeezed mechanical state by time-continuous teleportation. The protocols
presented here are feasible in optomechanical systems exhibiting a
cooperativity larger than 1.
