Finite-key security analysis of the 1-decoy state QKD protocol with a leaky intensity modulator

The finite-key security of the standard three-intensity decoy-state quantum key distribution (QKD) protocol in the presence of information leakage has been analyzed (Wang et al. in New J Phys 20:083027, 2018). On the other hand, the 1-decoy state QKD protocol has been proved to be able to achieve higher secret key rate than the three-intensity decoy-state QKD protocol in the finite-key regime by using only two different intensity settings (Davide et al. in Appl Phys Lett 112:171104, 2018). In this work, we analyze the finite-key security of the 1-decoy state QKD protocol with a leaky intensity modulator, which is used to generate the decoy state. In particular, we simulate the secret key rate under three practical cases of Trojan-horse attacks. Our simulation results demonstrate that the 1-decoy state QKD protocol can be secure over long distances within a reasonable time frame given that the intensity modulator is sufficiently isolated. By comparing the simulation results to those presented in Wang et al. (2018), we find that, as expected, the 1-decoy state QKD protocol is more robust against information leakage from the intensity modulator for all achievable distances.