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We show that the closed-loop control obtained by feeding back the derivativeof the signal from the homodyne measurement of one mode of the light exiting atwo-mode optical cavity interacting with a mechanical resonator permits tocontrol and increase optical output entanglement. In particular, the proposedfeedback-enhanced setup allows to achieve a fidelity of coherent stateteleportation 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 inpresence of loss, which otherwise would not be possible without feedback

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