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Journal of Physics Conference Series

A continuous variable quantum key distribution protocol based on multi-dimensiondata reconciliation with Polar code

Feng Bao, Chao Lv, Jinsuo Liu, Tianbing Zhang

Published Jan 1, 2021• 3 citations

Abstract

Abstract The continuous variable quantum key distribution protocol (CV-QKD) has the advantages of easy generation of quantum signals, convenient measurement and high communication capacity. However, the multi-dimensional data reconciliation is mainly implemented by binary LDPC code as quantum error correction code, which is greatly affected by complex environments and the bit error rate is high. In order to solve this problem, acontinuous variable quantum key distribution protocol based onmulti-dimension data reconciliation with Polar code, that can be applied to long-distance transmission in power systems, is proposed. First, we prepare an EPR quantum state, and perform heterodyne detection on one of the quantum states, and obtain the values of two orthogonal components at the same time which is the coherent state of the information carrier. Then the continuous variable quantum key distribution is realized by six steps (i.e., quantum state preparation, gaussian random detection, data filtering, calculation of bit error rate, data reconciliation, privacy amplification).In data reconciliation, we use Polar code as the error correction code and use reverse coding technology to achieve key error correction, which can effectively improve the negotiation efficiency. Numerical simulation verifies the feasibility of the protocol, and the protocol is more efficient than the multi-dimensiondata reconciliation protocol based on LDPC code under the same conditions.

DOI: 10.1088/1742-6596/1757/1/012111

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A challenging issue in continuous-variable quantum key distribution (CV-QKD) is the improvement in error correction efficiency because random number bits are encoded in a quadrature of faint optical pulses. Herein, we propose an error-control information reconciliation method for CV-QKD based on our recently proposed fixed-bit polar code. In the present scheme, unreliable bits are embedded in the prepared “fixed bits,” enabling the detection and reproduction of errors in these bits without error correction, effectively improving the error-correction efficiency. Numerical simulations demonstrate that the efficiency of the proposed scheme is 10% higher than that of polar code-based reconciliation without fixed bits.

Information reconciliation is a significant step for a continuous-variable quantum key distribution (CV-QKD) system. We propose a reconciliation method that allows two authorized parties to extract a consistent and secure binary key in a CV-QKD protocol, which is based on Gaussian-modulated coherent states and homodyne detection. This method named spherical reconciliation is based on spherical quantization and non-binary low-density parity-check (LDPC) codes. With the suitable signal-to-noise ratio (SNR) and code rate of non-binary LDPC codes, spherical reconciliation algorithm has a high efficiency and can extend the transmission distance of CV-QKD.

Reconciliation is an essential procedure for continuous-variable quantum key distribution (CV-QKD). As the most commonly used reconciliation protocol in short-distance CV-QKD, the slice error correction (SEC) allows a system to distill more than 1 bit from each pulse. However, the quantization efficiency is greatly affected by the noisy channel with a low signal-to-noise ratio (SNR), which usually limits the secure distance to about 30 km. In this paper, an improved SEC protocol, named Rotated-SEC (RSEC), is proposed through performing a random orthogonal rotation on the raw data before quantization, and deducing a new estimator for the quantized sequences. Moreover, the RSEC protocol is implemented with polar codes. The experimental results show that the proposed protocol can reach up to a quantization efficiency of about 99%, and maintain at around 96% even at the relatively low SNRs (0.5,1), which theoretically extends the secure distance to about 45 km. When implemented with the polar codes with a block length of 16 Mb, the RSEC achieved a reconciliation efficiency of above 95%, which outperforms all previous SEC schemes. In terms of finite-size effects, we achieved a secret key rate of 7.83×10-3 bits/pulse at a distance of 33.93 km (the corresponding SNR value is 1). These results indicate that the proposed protocol significantly improves the performance of SEC and is a competitive reconciliation scheme for the CV-QKD system.

Continuous-variable quantum key distribution (CV-QKD) requires highly efficient reconciliation techniques to operate at low signal-to-noise ratios and long distances. Multidimensional reconciliation addresses this challenge by transforming the physical Gaussian quantum channel into a virtual binary-input additive white Gaussian noise (BIAWGN) channel, enabling the use of modern errorcorrecting codes. In this work, we review the principles of multidimensional reconciliation, with a particular focus on high-dimensional constructions beyond the algebraic dimensions 1, 2, 4, 8. We describe the construction of the virtual channel, discuss practical coding schemes for reverse reconciliation, and analyse their integration with linear error-correcting codes. We also present an opensource simulation framework, HDirac, implementing multidimensional reconciliation for arbitrary dimensions, and use it to evaluate state-of-the-art LDPC codes. The results highlight key trade-offs between dimension, reconciliation efficiency, and frame error rate, providing practical guidance for CV-QKD system design.

Abstract The error correction of information reconciliation affects the performance of the continuous-variable quantum key distribution (CV-QKD). Polar codes can be strictly proven to reach the Shannon-limit. However, due to the insufficient polarization of finite code-length, partial subchannels are neither completely noise-free nor completely noisy. In this paper, an intermediate channel low-density parity check code concatenated polar code (IC-LDPC Polar codes)-based reconciliation for CV-QKD is proposed for the above shortcomings. The experimental results show that the reconciliation efficiency of IC-LDPC Polar code can be over 98% when the signal-to-noise ratio is from −13.2 dB to −20.8 dB, the secret keys can be extracted, and the minimum frame error rate (FER) is 0.19. Therefore, the proposed scheme can improve the reconciliation efficiency and reduce the FER at a very low signal-to-noise ratio range, and it is more useful for a practical long-distance CV-QKD system.