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Acta Optica Sinica

Multidimensional Reconciliation for Continuous-Variable Quantum Key Distribution Based on Two-Edge Type Low-Density Parity-Check Codes

马识途 Ma Shitu, 郭大波 Guo Dabo, 薛哲 Xue Zhe, 贺超 He Chao

Published Jan 1, 2019• 0 citations
Publisher
DOI
10.3788/aos201939.0527001

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Continuous-variable quantum key distribution (QKD) utilizes an ensemble of coherent states of light to distribute secret encryption keys between two parties. An essential ingredient of the QKD protocol is highly efficient information reconciliation. To achieve highly efficient reconciliation, error-correcting codes with a low channel coding rate are inevitable in the most common schemes of multilevel coding and multistage decoding (MLC-MSD) and multidimensional reconciliation. Multiedge-type (MET) low-density parity-check (LDPC) codes are well suited for highly efficient reconciliation at low rates. Here, we calculate the optimal channel coding rates in the MLC-MSD scheme for reverse reconciliation, introduce the concept of generalized extrinsic information transfer charts for MET-LDPC codes, which constitute a simple and fast asymptotic analysis tool, and present a set of MET-LDPC codes with asymptotic efficiency >97>97%>97 for channel coding rates 0.1, 0.05, 0.02, and 0.01. We believe that our codes will find wide application in implementations of continuous-variable quantum key distribution based on Gaussian modulation.
Achieving information theoretic security with practical complexity is of great interest to continuous-variable quantum key distribution in the postprocessing procedure. In this paper, we propose a reconciliation scheme based on the punctured low-density parity-check (LDPC) codes. Compared to the well-known multidimensional reconciliation scheme, the present scheme has lower time complexity. Especially when the chosen punctured LDPC code achieves the Shannon capacity, the proposed reconciliation scheme can remove the information that has been leaked to an eavesdropper in the quantum transmission phase. Therefore, there is no information leaked to the eavesdropper after the reconciliation stage. This indicates that the privacy amplification algorithm of the postprocessing procedure is no more needed after the reconciliation process. These features lead to a higher secret key rate, optimal performance, and availability for the involved quantum key distribution scheme.