Feedback Control of Two-mode Output Entanglement and Steering in Cavity Optomechanics

We show that the closed-loop control obtained by feeding back the derivative of the signal from the homodyne measurement of one mode of the light exiting a two-mode optical cavity interacting with a mechanical resonator permits to control and increase optical output entanglement. In particular, the proposed feedback-enhanced setup allows to achieve a fidelity of coherent state teleportation greater than the threshold value of 2/3 for secure teleportation, and two-way steering between the two cavity's output modes down the line in presence of loss, which otherwise would not be possible without feedback