I. INTRODUCTION

II. PREPARE-AND-MEASURE PHOTON SUBTRACTION-BASED MDI CV-QKD SCHEME

III. THE EQUIVALENT ENTANGLEMENT ASSISTED PHOTON SUBTRACTION-BASED MDI CV-QKD SCHEME AND CORRESPONDING COVARIANCE MATRICIES

IV. THE SECRET-KEY RATE CALCULATIO

V. ILLUSTRATIVE SECRET-KEY RATE RESULT

VI. CONCLUDING REMARKS

REFERENCES

To potentially overcome the practical security loopholes of CV-QKD protocols, in this paper, we propose to use the optimized eight-state measurement-device-independent (MDI) protocol and demonstrate that it can significantly outperform corresponding Gaussian modulation-based MDI and virtual photon subtraction-based MDI CV-QKD protocols in terms of both secret-key rate and achievable transmission distance. Contrary to the common belief that virtual photon subtraction method can extend the distance of MDI CV-QKD protocols, we show that this is not true for fully optimized MDI CV-QKD protocols and realistic system parameters.

INTRODUCTION

The quantum key distribution (QKD) leverages the principles of quantum mechanics to realize the distribution of keys with security that can be verified [1]–[۸]. Various QKD schemes can be placed into two broad categories: discrete variable (DV) and continuous variable (CV) QKD schemes. DV-QKD employs the photon counting, followed by the postelection to identify signaling intervals when the detection takes place [7]. These schemes are affected by the long dead time of the single-photon detectors (SPDs), high dark current rate, and insufficient quantum efficiency. In contrast, the CV-QKD employs either homodyne or heterodyne detection. The long deadtime of SPDs, used in DV-QKD schemes, limits the baud rate and consequently the secret-key rate (SKR). Given that CV-QKD schemes employ the homodyne/heterodyne detection instead, they do not exhibit the deadtime problem. The CV-QKD protocols are typically implemented based on Gaussian modulation (GM) [9]–[۱۴] or discrete modulation (DM) [15]–[۱۹]. (An interested reader interested in differences between GM-based and DM-based CV-QKD schemes is referred to refs. [6] and [7].) The security analysis of CV-QKD schemes typically relies on idealized assumptions, which are very difficult to satisfy in practice. Any imperfection in practical devices yields to the security loophole that can be exploited by Eve to compromise security.