Phase-noise estimation using Bayesian inference for discretely modulated measurement-device-independent continuous-variable quantum key distribution

Measurement-device-independent continuous-variable quantum key distribution (MDI-CVQKD) protocol calibrates the phase reference frames by transmitting local oscillator pulses between two legitimate parties. The above implementation leaves massive loopholes; in particular, an eavesdropper can attack the system by manipulating the power of the local oscillator pulses. In this paper, a Bayesian phase-noise estimation model is proposed to estimate the phase drift and its uncertainty in the MDI-CVQKD protocol. The model employs the Bayesian estimation of the very weak quantum signal pulses and eliminates the necessity of transmitting local oscillator pulses between two legitimate parties. Moreover, the Bayesian inference algorithm has the characteristic of high robustness to noise and can achieve a well-motivated confidence interval of the estimated eigenphase. Comparing with its Gaussian counterpart, we adopt the discrete modulation in the MDI-CVQKD protocol, which allows a much better reconciliation efficiency at low signal-to-noise ratio. With simpler implementation, the proposed Bayesian phase-noise estimation model precisely avoids the security bottleneck due to the transmitted local oscillator pulses.