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 us to control and increase optical output entanglement. In particular, the proposed feedback-enhanced setup allows us 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 cavities' output modes down the line in the presence of loss, which otherwise would not be possible without feedback.