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We study the measurement device independent quantum key distribution (MDIQKD)in practice with limited resource, when there are only 3 different states inimplementing the decoy-state method and when there are basis dependent codingerrors. We present general formulas for the decoy-state method for two-pulsesources with 3 different states, which can be applied to the recently proposedMDIQKD with imperfect single-photon source such as the coherent states or theheralded states from the parametric down conversion. We point out that theexisting result for secure QKD with source coding errors does not always hold.We find that very accurate source coding is not necessary. In particular, weloosen the precision of existing result by several magnitude orders for secureQKD.

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