Practical measurement-device-independent quantum key distribution without vacuum sources

Most of existing protocols for the decoy-state measurement-device-independent quantum key distribution use vacuum sources or extremely weak sources, but the laboratory cannot give real vacuum sources or precise extremely weak sources. We present a four-intensity protocol without using any of them. Our protocol gives a secure key rate close to those in the protocols with vacuum sources.

Figure 1

Optimized key rates (per pulse pair) versus transmission distance with different ${\mu }_{\omega }$ with device parameters given row 2 of Table 1. The total number of pulses at each side is $N_t={10}^{11}$ and we set the failure probability $\epsilon ={10}^{-7}$.

Figure 2

Optimized key rates (per pulse pair) versus transmission distance with different methods and different ${\mu }_{\omega }$ with device parameters given in row 3 of Table 1. The total number of pulses at each side is $N_t={10}^{12}$ and we set the failure probability $\epsilon ={10}^{-7}$.

Figure 3

Optimized key rates (per pulse pair) versus transmission distance with different methods and different ${\mu }_{\omega }$ with device parameters given in row 1 of Table 1. The total number of pulses at each side is $N_t={10}^{10}$ and we set the failure probability $\epsilon ={10}^{-7}$.