Three-intensity decoy-state method for device-independent quantum key distribution with basis-dependent errors

Abstract

We study the measurement-device-independent quantum key distribution (MDIQKD) in practice with limited resources when there are only three different states in implementing the decoy-state method and when there are basis-dependent coding errors. We present general formulas for the decoy-state method for two-pulse sources with three different states, which can be applied to the recently proposed MDIQKD with imperfect single-photon sources such as the coherent states or the heralded states from the parametric down-conversion. We point out that the existing result for secure MDIQKD with source coding errors does not always hold. We find that very accurate source coding is not necessary. In particular, we loosen the precision of the existing result by several orders of magnitude.