LQG measurement-feedback control of distributed entanglement generation between continuous-mode Gaussian fields

This paper studies a scheme of two spatially distant oscillator systems that are connected by Gaussian fields and examines distributed entanglement generation between two continuous-mode output Gaussian fields that are radiated by the oscillators. It is demonstrated that using measurement-feedback control while a non-local effective entangling operation is on can help to enhance the Einstein-Podolski-Rosen (EPR)-like entanglement between the output fields. The effect of propagation delays and losses in the fields interconnecting the two oscillators, and the effect of other losses in the system, are also considered. In particular, for a range of time delays the measurement feedback controller is able to maintain stability of the closed-loop system and the entanglement enhancement, but the achievable enhancement is only over a smaller bandwidth that is commensurate with the length of the time delays.