Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2106.06206

Rotation Based Slice Error Correction Protocol for Continuous-variable Quantum Key Distribution and its Implementation with Polar Codes

Xuan Wen, Qiong Li, Haokun Mao, Xiaojun Wen, Nan Chen

Published Jun 11, 2021• 3 citations
arXivHTMLPDF

Abstract

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, its 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 Rotation-based SEC (RSEC), is proposed through performing a random orthogonal rotation on the raw data before quantization, and deducing a new estimator for quantized sequences. Moreover, the RSEC protocol is implemented with polar codes. Experimental results show that the proposed protocol can reach up to a quantization efficiency of about 99\%, and maintains 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 block length of 16 Mb, the RSEC can achieve a reconciliation efficiency of above 95\%, which outperforms all previous SEC schemes. In terms of finite-size effects, we achieve a secret key rate of $7.83\times10^{-3}$ 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.

DOI
10.48550/arxiv.2106.06206

Related papers

An Improved Slice Reconciliation Protocol for Continuous-Variable Quantum Key Distribution

Xuan Wen, Qiong Li, Haokun Mao +2 more

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.

Entropy•Oct 9, 2021•10 citations

A novel slice error correction reconciliation for continuous-variable quantum key distribution

Lin Zhu, Xueqin Jiang, Han Hai +3 more

Information reconciliation is a crucial process in continuous-variable quantum key distribution(CV-QKD) systems. The slice error correction (SEC) reconciliation is appropriate for short-distance CV-QKD. However, the efficiency of SEC reconciliation schemes is significantly influenced by noisy channels with low signal-to-noise ratios (SNRs). In this paper, we present an enhanced information reconciliation scheme, termed AC-SEC reconciliation, which adds the new Gaussian sequences c with the original Gaussian sequences y before quantization in the SEC reconciliation to obtain secret key sequences with high variance and reduce noise interferences. Simulation results demonstrate that compared with the traditional SEC reconciliation, the proposed information reconciliation has lower frame error rate (FER) and higher reconciliation efficiency, which can increase the secret key rate (SKR).

International Conference on Quantum Communications, Networking, and Computing (QCNC)•Mar 31, 2025•0 citations

Continuous-variable quantum key distribution with low-complexity information reconciliation

Xiangyu Wang, Hongjie Wang, Chao Zhou +3 more

Information reconciliation is an essential step of continuous-variable quantum key distribution (CV-QKD) because its efficiency affects both the maximum transmission distance and the final secret key rate of the whole system. Slice reconciliation can achieve high secret key rates for the CV-QKD systems under high signal-to-noise ratios (SNRs). However, it suffers from the high designing cost of the error-correcting codes in the multi-level coding and multi-stage decoding step. To reconcile one set of data with fixed SNR, multiple error-correcting codes with different code rates need to be designed. If the channel environment changed, the code rates need to change along to maintain high reconciliation efficiency, making it complicated and costly. In this paper, we introduce polar codes into slice reconciliation and proposed a scheme that is simply constructed, effectively performed, and well adapted to the systems with wide-range and variational SNRs. Simulation results show that the proposed scheme offers reconciliation efficiency over 95% for the systems with SNRs range from 1 to 10, which can support the systems with high secret key rates. The decrease of complexity and the increase of secret key rate have great significance for a practical CV-QKD system.

Optics Express•Jul 21, 2022•32 citations

IC-LDPC Polar codes-based reconciliation for continuous-variable quantum key distribution at low signal-to-noise ratio

Zhengwen Cao, Xinlei Chen, Geng Chai +1 more

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.

Laser Physics Letters•Feb 14, 2023•11 citations

Short-block polar coding based CV-QKD reconciliation

Dingzhao Wang

Continuous-variable quantum key distribution (CV-QKD) offers an attractive route to information-theoretic secure communications using coherent detection and largely off-the-shelf telecommunication components. However, practical deployment remains constrained by the efficiency and reliability of information reconciliation in the low signal-to-noise ratio (SNR) regime, finite block-length effects, and the need to operate robustly under time-varying channels. This thesis addresses these challenges by developing short-block polar-coded reconciliation schemes, an adaptive incremental-redundancy hybrid automatic repeat request (IR-HARQ) framework tailored to CV-QKD, and a simultaneous quantum and classical communication (SQCC) architecture with joint classical--quantum optimization. Firstly, this thesis investigates polar codes as a finite-length alternative to conventional LDPC-based reconciliation. By constructing and evaluating a series of progressively enhanced reconciliation architectures, it is shown that short-block polar codes can provide improved block-error-rate (BLER) performance and higher reconciliation efficiency in the operating regime relevant to practical CV-QKD systems. The study further analyzes implementation trade-offs, including computational load distribution between Alice and Bob and the impact of decoder choices, identifying list decoding with moderate list sizes as an effective performance--complexity compromise. Secondly, to address channel variability and the sensitivity of fixed-rate reconciliation at low SNR, an IR-HARQ reconciliation protocol is proposed. Instead of committing to a single code rate, the protocol progressively reveals additional redundancy across retransmissions, effectively lowering the coding rate only when needed. A reliability-driven frozen-bit scheduling strategy is developed to maximize the error-correction benefit per disclosed bit under finite-length constraints, while ensuring that the resulting leakage is properly accounted for in privacy amplification. The proposed IR-HARQ design significantly improves reconciliation robustness and extends the achievable secure distance compared with one-shot fixed-rate baselines. Thirdly, this thesis considers SQCC, where classical data transmission and CV-QKD share the same physical link. A power-allocation model is established through the power ratio between the quantum and classical components, and the resulting classical and quantum error behaviors are characterized. By incorporating successive interference cancellation and forward error correction on both components, the proposed SQCC designs enable simultaneous classical throughput and secure key generation with controllable trade-offs among reliability, excess noise, and secret key rate. Overall, the thesis demonstrates that short-block polar coding, when combined with adaptive IR-HARQ and SQCC-aware receiver processing, provides a coherent framework for improving the practicality of CV-QKD under finite-length and time-varying conditions, thereby supporting more resource-efficient and deployable quantum-secured communication systems.

•Jan 1, 2026•0 citations

Rate-Adaptive Polar-Coding-Based Reconciliation for Continuous-Variable Quantum Key Distribution at Low Signal-to-Noise Ratio

Zhengwen Cao, Xinlei Chen, Geng Chai +2 more

Information reconciliation significantly impacts the performance of the practical continuous-variable quantum key distribution (CV QKD) system. Fixed-rate error-correction codes limit the potential applications of the CV QKD because they lead to reduced reconciliation efficiency when the signal-to-noise ratio of the quantum channel changes, further deteriorating the system's performance. Therefore, we propose a rate-adaptive polar-coding-based reconciliation scheme for practical CV QKD systems with the time-variant quantum channel. Experimental results verify that the proposed scheme can successfully extract secret keys within the range of signal-to-noise ratios from $\ensuremath{-}0.5$ to $\ensuremath{-}4.5$ dB, and the minimum frame-error rate can be less than ${10}^{\ensuremath{-}3}$. Moreover, the proposed scheme can promote the application of the CV QKD system in a realistic environment.

Physical Review Applied•Apr 7, 2023•22 citations
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, its 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 Rotation-based SEC (RSEC), is proposed through performing a random orthogonal rotation on the raw data before quantization, and deducing a new estimator for quantized sequences. Moreover, the RSEC protocol is implemented with polar codes. Experimental results show that the proposed protocol can reach up to a quantization efficiency of about 99%, and maintains at around 96% even at the relatively low SNRs (0.5,1)(0.5,1)(0.5,1), which theoretically extends the secure distance to about 45 km. When implemented with the polar codes with block length of 16 Mb, the RSEC can achieve a reconciliation efficiency of above 95%, which outperforms all previous SEC schemes. In terms of finite-size effects, we achieve a secret key rate of 7.83×10−37.83\times10^{-3}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.
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.
Information reconciliation is a crucial process in continuous-variable quantum key distribution(CV-QKD) systems. The slice error correction (SEC) reconciliation is appropriate for short-distance CV-QKD. However, the efficiency of SEC reconciliation schemes is significantly influenced by noisy channels with low signal-to-noise ratios (SNRs). In this paper, we present an enhanced information reconciliation scheme, termed AC-SEC reconciliation, which adds the new Gaussian sequences c with the original Gaussian sequences y before quantization in the SEC reconciliation to obtain secret key sequences with high variance and reduce noise interferences. Simulation results demonstrate that compared with the traditional SEC reconciliation, the proposed information reconciliation has lower frame error rate (FER) and higher reconciliation efficiency, which can increase the secret key rate (SKR).
Information reconciliation is an essential step of continuous-variable quantum key distribution (CV-QKD) because its efficiency affects both the maximum transmission distance and the final secret key rate of the whole system. Slice reconciliation can achieve high secret key rates for the CV-QKD systems under high signal-to-noise ratios (SNRs). However, it suffers from the high designing cost of the error-correcting codes in the multi-level coding and multi-stage decoding step. To reconcile one set of data with fixed SNR, multiple error-correcting codes with different code rates need to be designed. If the channel environment changed, the code rates need to change along to maintain high reconciliation efficiency, making it complicated and costly. In this paper, we introduce polar codes into slice reconciliation and proposed a scheme that is simply constructed, effectively performed, and well adapted to the systems with wide-range and variational SNRs. Simulation results show that the proposed scheme offers reconciliation efficiency over 95% for the systems with SNRs range from 1 to 10, which can support the systems with high secret key rates. The decrease of complexity and the increase of secret key rate have great significance for a practical CV-QKD system.
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.
Continuous-variable quantum key distribution (CV-QKD) offers an attractive route to information-theoretic secure communications using coherent detection and largely off-the-shelf telecommunication components. However, practical deployment remains constrained by the efficiency and reliability of information reconciliation in the low signal-to-noise ratio (SNR) regime, finite block-length effects, and the need to operate robustly under time-varying channels. This thesis addresses these challenges by developing short-block polar-coded reconciliation schemes, an adaptive incremental-redundancy hybrid automatic repeat request (IR-HARQ) framework tailored to CV-QKD, and a simultaneous quantum and classical communication (SQCC) architecture with joint classical--quantum optimization. Firstly, this thesis investigates polar codes as a finite-length alternative to conventional LDPC-based reconciliation. By constructing and evaluating a series of progressively enhanced reconciliation architectures, it is shown that short-block polar codes can provide improved block-error-rate (BLER) performance and higher reconciliation efficiency in the operating regime relevant to practical CV-QKD systems. The study further analyzes implementation trade-offs, including computational load distribution between Alice and Bob and the impact of decoder choices, identifying list decoding with moderate list sizes as an effective performance--complexity compromise. Secondly, to address channel variability and the sensitivity of fixed-rate reconciliation at low SNR, an IR-HARQ reconciliation protocol is proposed. Instead of committing to a single code rate, the protocol progressively reveals additional redundancy across retransmissions, effectively lowering the coding rate only when needed. A reliability-driven frozen-bit scheduling strategy is developed to maximize the error-correction benefit per disclosed bit under finite-length constraints, while ensuring that the resulting leakage is properly accounted for in privacy amplification. The proposed IR-HARQ design significantly improves reconciliation robustness and extends the achievable secure distance compared with one-shot fixed-rate baselines. Thirdly, this thesis considers SQCC, where classical data transmission and CV-QKD share the same physical link. A power-allocation model is established through the power ratio between the quantum and classical components, and the resulting classical and quantum error behaviors are characterized. By incorporating successive interference cancellation and forward error correction on both components, the proposed SQCC designs enable simultaneous classical throughput and secure key generation with controllable trade-offs among reliability, excess noise, and secret key rate. Overall, the thesis demonstrates that short-block polar coding, when combined with adaptive IR-HARQ and SQCC-aware receiver processing, provides a coherent framework for improving the practicality of CV-QKD under finite-length and time-varying conditions, thereby supporting more resource-efficient and deployable quantum-secured communication systems.
Information reconciliation significantly impacts the performance of the practical continuous-variable quantum key distribution (CV QKD) system. Fixed-rate error-correction codes limit the potential applications of the CV QKD because they lead to reduced reconciliation efficiency when the signal-to-noise ratio of the quantum channel changes, further deteriorating the system's performance. Therefore, we propose a rate-adaptive polar-coding-based reconciliation scheme for practical CV QKD systems with the time-variant quantum channel. Experimental results verify that the proposed scheme can successfully extract secret keys within the range of signal-to-noise ratios from $\ensuremath{-}0.5$ to $\ensuremath{-}4.5$ dB, and the minimum frame-error rate can be less than ${10}^{\ensuremath{-}3}$. Moreover, the proposed scheme can promote the application of the CV QKD system in a realistic environment.