Novel reconciliation protocol based on spinal code for continuous-variable quantum key distribution

Reconciliation is a crucial procedure in post-processing of continuous-variable quantum key distribution (CV-QKD) system, which is used to make two distant legitimate parties share identical corrected keys. The adaptive reconciliation is necessary for practical systems to cope with the variable channel. Many researchers adopt fixed-rate error correction codes to implement adaptive reconciliation, such as the punctured LDPC code; however such protocol can achieve high efficiency only in a small range of signal-to-noise ratios (SNRs). In this paper, the spinal-based rateless reconciliation protocol for CV-QKD is first proposed. The proposed adaptive reconciliation protocol can achieve high efficiency in a much larger range of SNRs. Because the protocol we propose uses the code with short length and simple encoding/decoding structure, the design and implementation complexities of our protocol are greatly decreased. Meanwhile, its parallel attribute makes it suitable for hardware implementation, which means it has the potential of achieving high-throughput reconciliation. Moreover, the security of proposed protocol is investigated and proved. Experimental results show that the reconciliation efficiency of the spinal-based protocol maintains around 95%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$95\%$$\end{document} in a larger SNR range (0,0.5), and even exceeds 96.5%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$96.5\%$$\end{document} at extremely low SNR (≤0.032\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\le 0.032$$\end{document}) with quite low frame error rate (FER) (≤5.2%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\le 5.2\%$$\end{document}). Both the theoretical analysis and experimental results demonstrate that the proposed adaptive reconciliation protocol is a suitable candidate for the long-distance CV-QKD systems.