Long-distance continuous-variable measurement-device-independent quantum key distribution with discrete modulation

We propose a long-distance continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD) protocol with discrete modulation. This kind of discrete-modulated schemes have good compatibility with efficient error correction code, which lead to higher reconciliation efficiency even at low signal-to-noise ratio (SNR). Security analysis shows that the proposed protocol is secure against arbitrary collective attacks in the asymptotic limit with proper use of decoy states. And with the using of discrete modulation, the proposed CV-MDI-QKD protocol has simpler implementation and outperform previous protocols in terms of achievable maximal transmission distance, which precisely solve the bottleneck of the original Gaussian-modulated CV-MDI-QKD protocol.