Measurement-device-independent quantum key distribution with source state errors and statistical fluctuation

We show how to calculate the secure final key rate in the four-intensity decoy-state measurement-device-independent quantum key distribution protocol with both source errors and statistical fluctuations with a certain failure probability. Our results rely only on the range of only a few parameters in the source state. All imperfections in this protocol have been taken into consideration without assuming any specific error patterns of the source.

Figure 1

The optimal key rates (per pulse) versus transmission distance (the distance between Alice and Bob) with different intensity fluctuations under the experimental parameters listed in Table 1. Here we set the total number of pulses on each side as $N_t={10}^{11}$.

Figure 2

The optimal key rates (per pulse) versus transmission distance (the distance between Alice and Bob) with different intensity fluctuations under the experimental parameters listed in Table 1. Here we set the total number of pulses on each side as $N_t={10}^{13}$ and the detection efficiency as ${\eta }_d=40.0\%$.