Improving long-distance distribution of entangled coherent state with the method of twin-field quantum key distribution

The twin-field quantum key distribution (TFQKD) protocol has garnered considerable attention in quantum communication because it overcomes the well-known fundamental limit of the secret key rate without quantum repeaters. In this study, we employ this scheme to demonstrate the long-distance distribution of entangled coherent state (ECS), which has not been addressed in the existing literature. We show a scheme for the distribution of ECS with a yield of ^√η, where η is the total efficiency of the whole transmission link. Compared to the cat-state based scheme, the success probability for fidelity is enhanced by 1.86 to 11.54 times in our new scheme, where the ECS is |ψ_ECS(α = 2.0)i and the fixed fidelity (F) ranges from 0.99 to 0.75. The performance of our scheme in the presence of realistic on-off photon detector has also been investigated. Our work provides the application of TFQKD method toward continuous variable entanglement distribution and we believe that its application to other quantum information processing protocols are worth investigation in the near future.