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Phase reference calibration is a necessary procedure in practical continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD) for the need of Bell-State Measurement (BSM). However, the phase reference calibration may become imperfect in practical applications. We explored the practical security of CV-MDI-QKD with imperfect phase reference calibration under realistic conditions of lossy and noisy quantum channel. Specifically, a comprehensive framework is developed to model and characterize the imperfection of practical phase reference calibration operation, which is mainly caused by the non-synchronization of two remote lasers in senders. Security analysis shows that the imperfect phase reference calibration has significant side effects on the performance and security of the CV-MDI-QKD protocol. A tight security bound to excess noise introduced by imperfect phase reference calibration is derived for reverse reconciliation against arbitrary collective attacks in the asymptotic limit, and the tolerance of the CV-MDI-QKD protocol to this excess noise is also obtained. This security analysis framework can eliminate the security hazards caused by imperfect phase reference calibration without changing the existing CV-MDI-QKD system structure., Comment: 10 pages, 9 figures

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., Comment: 8 pages, 5 figures

It has been found that non-Gaussian operations can be applied to increase and distill entanglement between Gaussian entangled states. We show the successful use of the non-Gaussian operation, in particular, photon subtraction operation, on the continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD) protocol. The proposed method can be implemented based on existing technologies. Security analysis shows that the photon subtraction operation can remarkably increase the maximal transmission distance of the CV-MDI-QKD protocol, which precisely make up for the shortcoming of the original CV-MDI-QKD protocol, and 1-photon subtraction operation has the best performance. Moreover, the proposed protocol provides a feasible method for the experimental implementation of the CV-MDI-QKD protocol., Comment: 8 pages, 9 figures