Security Analysis of Sending or Not-Sending Twin-Field Quantum Key Distribution with Weak Randomness

Sending-or-not sending twin-field quantum key distribution (SNS TF-QKD) has the advantage of tolerating large amounts of misalignment errors, and its key rate can exceed the linear bound of repeaterless quantum key distribution. However, the weak randomness in a practical QKD system may lower the secret key rate and limit its achievable communication distance, thus compromising its performance. In this paper, we analyze the effects of the weak randomness on the SNS TF-QKD. The numerical simulation shows that SNS TF-QKD can still have an excellent performance under the weak random condition: the secret key rate can exceed the PLOB boundary and achieve long transmission distances. Furthermore, our simulation results also show that SNS TF-QKD is more robust to the weak randomness loopholes than the BB84 protocol and the measurement-device-independent QKD (MDI-QKD). Our results emphasize that keeping the randomness of the states is significant to the protection of state preparation devices.