An improved phase compensation noise model for the continuous-variable quantum key distribution with real local oscillators

In the continuous-variable quantum key distribution with real local oscillators, the reference pulses transmitted in the insecure quantum channel results in phase compensation noises on the homodyne detection of quantum signals. Traditionally, the phase compensation noise is modelled as a zero-mean Gaussian distribution for simplicity. However, it is more likely to be the one with non-zero mean in the actual environment. In this paper, the phase compensation noise is considered to be with a non-zero mean, and then the secure bound is analyzed according to the imperfect phase compensation noise model. The actual transmittance and excess noise are compared between the evaluation values derived from the theoretical analysis and the estimation values calculated by training signals. Simulation results show that the security analysis is consistent with the practical implementation, and the secret key rate decreases with the increasing mean value and noise variance.