# Sending-or-Not-Sending Twin-Field Quantum Key Distribution with Light Source Monitoring
## 1 Introduction  
Quantum key distribution (QKD) provides a way for different communication parties to share a set of identical security keys [1; 2]. The security of QKD is based on the laws of quantum physics and has been proved theoretically in different ways in the past decades. In addition to security analysis, people have also started to study the performance of QKD and to further improve the performance of real-life QKD systems by proposing new protocols [3; 4; 5; 6; 7]. Among all proposed protocols, measurement-device-independent (MDI) protocol is meaningful, since it can make up all the security loopholes in the detection part of QKD systems [8]. MDI protocol has developed rapidly in recent years, with many achievements obtained [9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19]. In theory, the application of the decoy state method [20] has been further studied, and more optimized parameter estimation results are obtained to achieve a better performance [9; 10; 11]. Besides, different MDI experiment schemes have been proposed [12] and several meaningful experiment achievements, including the field test [13] and the network experiment [14] based on the MDI protocol, have been carried out. Meanwhile, the continuous-variable MDI protocol has also been developed [16; 17; 18; 19]. With the developing of experimental research, the MDI protocol achieved a transmission distance of 404 km in 2016, which was the farthest distance for standard QKD at that time [15]. The transmission distance of QKD has been further increased recently. Based on the MDI protocol, an extraordinary protocol called twin-field quantum key distribution (TF-QKD) was proposed byLucamarini et al. in 2018, which can increase the transmission distance to over 550 km on standard optical fibers without quantum repeaters [21]. Because of its outstanding advantage in transmission distance, TF-QKD has recently been the subject of a lot of follow-up research [22; 23; 24; 25; 26; 27; 28; 29]. Actually, in the original protocol, the phase randomization process will lead to secure issues since the information of random phase is announced to Eve in the post-selection process [30]. In further research, different types of modified TF-QKD protocols have been proposed to improve the incomplete security analysis [22; 23; 24; 25; 26]. Through classifying the signals [22], or adding an extra test mode [23], or using a pre-selected global phase [25; 26], the security loophole of the post-selected part can be resolved. With the modified protocols, long-distance TF-QKD experiments have already been implemented [28; 29]. Recently, an exciting experimental work has shown that the transmission distance for TF-QKD can reach over 500 km in practice [28], showing that TF-type protocols can significantly improve the transmission distance with the currently available technology. Among those TF-type protocols, the sending-or-not-sending (SNS) protocol proposed by [PERSON] et al. is an effective scheme to combine with the decoy state method to solve the phase randomization problem. In the SNS protocol, there is no post-selection process for the random phases of the signal bits, which are used to generate the final secret keys, thus the problem is avoided [22]. By optimizing the proportion of the sending and not-sending signals, the SNS protocol can still achieve a very long transmission distance. A remaining problem with the SNS protocol is that the prepared quantum state in the source is assumed to be an ideal coherent state. Actually, the assumption could be broken since the prepared state will deviate from the ideal coherent state due to the non-ideality of the practical laser [31]. Moreover, since the light source structure in the SNS protocol is similar to the BB84 protocol, there will also be an untrusted source problem [32; 33; 34; 35; 36] in the source part, causing the photon number distribution (PND) of the light source to be unknown, and the prepared state to no longer be a coherent state.