Mode pairing quantum key distribution with light source monitoring

Mode pairing quantum key distribution (MP-QKD) overcomes the repeaterless bound without requiring phase locking and phase tracking. However, MP-QKD still assumes that the light source is trusted, which can present challenges in practical deployments and potentially introduce security vulnerabilities. In this paper, we propose a light source monitoring (LSM) scheme that guarantees the security of MP-QKD with the untrusted light sources. The simulation results demonstrate that, when considering untrusted light sources, the performance of MP-QKD with the LSM scheme remains nearly identical to that of ideal MP-QKD, even in the presence of the source fluctuations. Furthermore, we simplify some of the complex integration calculations involved in simulating the observed quantities of MP-QKD, which reduces the running time of the parameter optimization procedure.