Huiping Tian

Continuous-variable quantum key distribution (CV-QKD) provides a way for two remote participants called Alice and Bob to establish symmetric keys through an unsafe channel \cite{weedbrook2012gaussian,grosshans2003quantum}. Continuous-variable quantum key distribution (CV-QKD) based on commercial devices such as lasers and coherent detectors is moving towards practical. Experimental implementation of the CV-QKD systems using Gaussian-modulated coherent states (GMCS) has made significant progress recently \cite{zhang2019continuous}. At the mean time, the problems of performance degradation caused by imperfections of those experimental devices remain unsolved absolutely \cite{pirandola2020advances}. A non-orthogonal measurement angular error between quadrature components $X$ and $P$ from coherent detection is always ignored in the current experimental scheme. The optical phase shifter that constantly rotates the local oscillator phase is a necessity in continuous-variable quantum key distribution systems using heterodyne detection. In previous experimental implementations, the optical phase shifter is generally regarded as an ideal passive optical device that perfectly rotates the phase of the electromagnetic wave of $90^\circ$ \cite{wang2020high}. However,under the action of external force, the fibre is stretched or compressed within the elastic deformation range, and parameters such as the fibre change's geometrical size and refractive index change, thus causing the phase change of the transmitted signal in the fibre. Therefore, the phase shifter is somewhat susceptible to environmental changes and can hardly shift the phase by $90^\circ$ exactly Considering this, we propose a concrete interpretation of measurement angular error in practical systems and the corresponding entanglement-based description. Simultaneously, an estimation method of the measurement angular error and corresponding compensation scheme are demonstrated in some ways. We conclude that measurement angular error severely degrades the security, but the proposed calibration and compensation method can significantly help improve the performance of the practical CV-QKD systems. Undoubtedly, it is worth observing that our work is to strengthen practical security resulted from devices' imperfection.