Phase-matching quantum key distribution with imperfect sources

The huge discrepancies between actual devices and theoretical assumptions severely threaten the security of quantum key distribution. Recently, a general new framework called the reference technique has attracted wide attention in defending against the imperfect sources of quantum key distribution. Here, the state preparation flaws, the side channels of mode dependencies, the Trojan horse attacks, and the pulse classical correlations are studied by using the reference technique on the phase-matching protocol. Our simulation results highlight the importance of the actual secure parameters choice for transmitters, which is necessary to achieve secure communication. Increasing the single actual secure parameter will reduce the secure key rate. However, as long as the parameters are set properly, the secure key rate is still high. Considering the influences of multiple actual secure parameters will significantly reduce the secure key rate. These actual secure parameters must be considered when scientists calibrate transmitters. This work is an important step towards the practical and secure implementation of phase-matching protocol. In the future, it is essential to study the main parameters, find out their maximum and general values, classify the multiple parameters as the same parameter, and give countermeasures.