Continuous-variable measurement-device-independent quantum key distribution with multi-ring discrete modulation

We propose a continuous-variable measurement-device-independent quantum key distribution with multi-ring discrete modulation (MR-CV-MDI-QKD) protocol. In our scheme, coherent states are allocated across distinct rings (amplitudes) in the phase space, and each ring is subjected to traditional M-symbol phase shift keying (MPSK) modulation. The analysis and simulation are given to demonstrate the security of our scheme under collective attacks. The results show that, compared with the traditional discrete modulated (DM)-CV-MDI-QKD where only the MPSK is used for modulation with a fixed amplitude, MR-CV-MDI-QKD can decrease the upper bound of the information accessible to an eavesdropper, thereby facilitating an extended transmission distance and increasing the secret key rate, furthermore, it exhibits a higher tolerance to diminished reverse reconciliation efficiency. This work provides an effective way for the practical implementation of the CV-MDI-QKD protocol.