  The advantage distillation (AD) method has proven effective in improving the
performance of quantum key distribution (QKD). In this paper, we introduce the
AD method into a recently proposed asynchronous measurement-device-independent
(AMDI) QKD protocol, taking finite-key effects into account. Simulation results
show that the AD method significantly enhances AMDIQKD, e.g., extending the
transmission distance by 16 km with a total pulse count of N = 7.24*10^13, and
enables AMDI-QKD, previously unable to generate keys, to generate keys with a
misalignment error rate of 10%. As the AD method can be directly integrated
into the current system through refined post-processing, our results facilitate
the practical implementation of AMDI-QKD in various applications, particularly
in scenarios with high channel losses and misalignment errors.
