Entanglement distribution using three-mode separable state with imperfect equipments

We show a scheme to distribute the entanglement by using three-mode separable Gaussian state prepared with imperfect equipments. The scheme achieves the aim that the entanglement is distributed between two distant parties with only Gaussian operations and linear optics elements. Moreover, we analyse the logarithmic negativity of the entanglement shared between the two parties when the systems are imperfect and arrive at the conclusion that the logarithmic negativity is asymptotically stable with fluctuations within a certain space range.