Practical long-distance twin-field quantum digital signatures

Quantum digital signatures (QDSs) play a crucial role in modern communication. Generally, the performance of QDSs depends on the key generation protocol (KGP). However, as a part of quantum key distribution (QKD), the KGP is restricted by the fundamental rate-loss bound (PLOB bound). Fortunately, recent work indicates that twin-field QKD (TF-QKD) can overcome this bound. In general, the users in standard decoy-state TF-QKD protocols are assumed to emit a weak coherent-state source with continuously randomized phase; however, this assumption is not practically available in experimental implementation and may open a security loophole for eavesdroppers. To bridge the gap between theory and practice, this work presents two practical TF-QDS protocols that can be realized with common optical components and further implemented in a quantum fibre network. One protocol uses a continuous-phase-randomized source but does not perform phase post-selection, called Protocol I . The other protocol uses a discrete-phase-randomized source with phase post-selection, called Protocol II . Numerical simulation results show that the two proposed TF-QDS protocols can improve the performance of QDS in terms of both the signature rate and secure transmission distance compared with BB84-QDS and measurement-device-independent QDS.