Robustness and symmetry of deterministic quantum entanglement swapping

In this paper, we present two quantum entanglement swapping schemes, a single-channel scheme and a dual-channel scheme, based on fiber channel transmission. We theoretically calculated the Einstein-Podolsky-Rosen- (EPR-) type variance and symmetry parameter factors of deterministic quantum entanglement swapping in these two schemes. By comparing the quantum entanglement swapping of the single- and dual-channel schemes, we show that the transmission distance of the dual-channel scheme is much longer than that of the single-channel scheme. Interestingly, the quantum correlation strength and symmetry of the two remote modes after deterministic quantum entanglement swapping are significantly improved when the optimal classical gain and loss efficiency of the loss channel are chosen. Moreover, the entanglement swapping will be robust and not suffer from sudden death when the entangled optical modes are transmitted in the lossy fiber channel. We also show that nonzero entanglement enables deterministic quantum entanglement swapping under both schemes when the EPR entanglement is a pure state. The two optimized schemes provide feasible technical references for long-distance metropolitan quantum communication.