Practical Measurement Angular Errors Analysis for Thermal-State Continuous-Variable Quantum Key Distribution

Thermal-state continuous-variable quantum key distribution (CV-QKD) of direct reconciliation with heterodyne detection can improve the robustness of the protocols. However, CV-QKD protocols require outlier detection, optical phase shifters are used to achieve orthogonal differentiation of the modes, but the actual optical phase shifters suffer from measurement angular errors, resulting in the imperfect phase. This kind of error degrades the security of the system. In this paper, we analyze the causes of measurement angular error and its impact on the secret key rate of the thermal-state CV-QKD protocols. We propose a compensation method to compensate for the effects of the measurement angular error and give a more complete secure analysis method under collective attack. The results obtained in this paper further improve the secure analysis under the thermal-state protocol and further enhance the performance of the system using the compensation method.