An efficient implementation of the decoy-state measurement-device-independent quantum key distribution with heralded single-photon sources

We study the decoy-state measurement-device-independent quantum key distribution using heralded single-photon sources. This has the advantage that the observed error rate in X basis is in higher order and not so large. We calculate the key rate and transmission distance for two cases: one using only triggered events, and the other using both triggered and non-triggered events. We compare the key rates of various protocols and find that our new scheme using triggered and non-triggered events can give higher key rate and longer secure distance. Moreover, we also show the different behavior of our scheme when using different heralded single-photon sources, i.e., in poisson or thermal distribution. We demonstrate that the former can generate a relatively higher secure key rate than the latter, and can thus work more efficiently in practical quantum key distributions.