Twin-Field Quantum Network Coding for Multi-Party Key Distribution

Quantum network coding enables multi-party quantum interactions over bottleneck channels. The communication distance is usually constrained by the instability of quantum states. Twin-field quantum key distribution is designed to improve the communication distance, but it can only be applied in point-to-point scenarios. In this paper, we propose a feasible twin-field quantum network coding scheme, which enables multi-party key distribution over long distance in networks with bottleneck channels. Firstly, a butterfly network model is designed for long-distance communication. Then, the coding method at each intermediate node is designed to overcome the limitations of bottleneck channels. Finally, the key rate and decoy-state transmission features are derived to demonstrate the security and efficiency advantages. Compared with the original point-to-point twin-field quantum key distribution protocol, the proposed scheme can distribute a group key among the four end nodes of the butterfly network with only one transmission round. The key rate R and the channel transmittance eta still satisfy R proportional to eta 1/2. Such results will extend the communication distance and provide a foundation for the construction of large-scale quantum networks.