Continuous-variable entanglement mediated by a thermal oscillator

Abstract

We discuss the deterministic Gaussian entangling procedure between continuous variables of two directly noninteracting oscillators. The oscillators can only couple to the same mediating oscillator, which is initially at arbitrary noisy state and can be lost after the procedure. Unitary idealization of the procedure can generate large entanglement for any initial thermal noise of the mediator, thanks to the quantum version of the geometric phase. The generation of entanglement may considerably change when the procedure contains a weak dissipation. A robustness of this entangling procedure for weak dissipation is therefore a basic test of feasibility, especially in the limit of noisy mediator. We theoretically confirm the basic robustness of entanglement generation. Moreover, we suggest a nontrivial numerical optimization of the entangling procedure to approach an absolute robustness. For the weak dissipation, the optimization allows complete avoiding of the impact of the mediator noise. The suggested entangling procedure is therefore verified to be sufficiently robust for further development of quantum transducers.