Satellite-based phase-matching quantum key distribution

Quantum key distribution (QKD) has been experimentally verified over fiber-based link. However, it still remains problems to be solved. The key rate of QKD protocol naturally degrades with the channel transmittance (η\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}) and the loss of fiber-based link increases exponentially with distance. It limits the scale of quantum communication network. Now phase-matching QKD (PM-QKD) modified from twin-field QKD has broken rate-distance limit and realized the goal that the key rate is dependent on the square root of the channel transmittance η\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( \sqrt{\eta }\right) $$\end{document}. Satellite-based QKD works in free space without restriction of space. The characters of satellite-based link can be analyzed by using he elliptical beam model. Here, we adopt PM-QKD over satellite-based link. The scheme overcomes not only rate-distance limit, but also the restriction of fiber-based link. In this work the performance of two kinds of links is given with different weather conditions. The satellite communication widow is under consideration. Furthermore, the effects of data size and source error are discussed. The optimization of parameters is given and the performance is improved after optimization. This work is helpful for satellite-based quantum communication experiments as a reference.