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

Acta Sinica Quantum Optica

Reverse Reconciliation of Quantum Gaussian Distributed Key

郭大波 Guo Dabo, 刘纲 LIU Gang, 张宁 Zhang Ning, 蔡虹 CAI Hong

Published Jan 1, 2013• 1 citation
Publisher

Abstract

The party Alice in a cryptograph system transmits coherent quantum signals to the party Bob,obtaining a series of correlated continuous Gaussian variables.The process to distill a binary key out of the correlated Gaussian variables that they share is called continuous-variable quantum key distribution(CVQKD).Reconciliation in CVQKD,i.e.,to correct differences between the correlated variables,is the key issue discussed in the paper.Based on both sliced error correction(SEC) protocol and multilevel coding/multistage decoding(MLC/MSD),reconciliation is implemented by LDPC code-based Slepian-Wolf CODEC.According to the proposed multilevel Tanner graph which depicts message transition of information,multistage iterative intrinsic and extrinsic information belief-propagation(LLR-BP) update formulae are derived.Three decoding modes of MSD are compared experimentally in convergence and performance.Simulation results show that the proposed algorithm can reconcile reliably 10000 continuous quantum variables with efficiency of 92.3% when SNR of the channel is above 2.5 dB.

DOI
10.3788/asqo20131903.0219

Related papers

Reconciliation of Quantum Gaussian Distributed Key based on Turbo Codes

郭大波 Guo Dabo, 张宁 Zhang Ning, 刘纲 LIU Gang

Two legitimate users of an encryption system,Alice and Bob,want to acquire the key from the related Gaussian continuous variables X and Y transferred through a quantum channel,by exchanging parts of information through an ideal public authorized channel,and they get consistent binary keys from the inconsistent X and Y.This process is referred to reconciliation.This paper builds a reconciliation scheme for continuous-variables quantum key distribution using Turbo codes as the primitive code,on the basis of Sliced Error Correction(SEC) and Multi Level coding/Multi Stage Decoding(MLC/MSD).Parity bits of Turbo code are employed as the redundant information in the Slepian-Wolf encoding and decoding scheme.The simulation results show that the reconciliation convergences when the SNR is 7dB above whilst the block size is 20000.

Acta Sinica Quantum Optica•Jan 1, 2013•1 citation

Reverse Reconciliation for Continuous Variable Quantum Key Distribution

Yongmin Li

Based on the Multilevel Codes/Multistage Decoding system,we achieved the reverse reconciliation for continuous variable quantum key distribution.Firstly,we show how to select the optimal quantization interval by maximizing the mutual information between the communicating parties.Then the optimal rate of each equivalent channel is calculated at the SNR level of 4 dB.The low-density parity check(LDPC) code is chosen as the channel codes,and the reverse reconciliation utilize a side-information based LDPC iterative decoding algorithm.

Acta Sinica Quantum Optica•Jan 1, 2012•0 citations

Multiedge-type low-density parity-check codes for continuous-variable quantum key distribution

Hossein Mani, Tobias Gehring, Philipp Grabenweger +3 more

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 $>97%$ 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.

arXiv:1812.05867•Physical Review A•Jun 25, 2021•37 citations

High-efficiency reconciliation for continuous variable quantum key distribution

Zengliang Bai, Shenshen Yang, Yongmin Li

Abstract Quantum key distribution (QKD) is the most mature application of quantum information technology. Information reconciliation is a crucial step in QKD and significantly affects the final secret key rates shared between two legitimate parties. We analyze and compare various construction methods of low-density parity-check (LDPC) codes and design high-performance irregular LDPC codes with a block length of 10 6 . Starting from these good codes and exploiting the slice reconciliation technique based on multilevel coding and multistage decoding, we realize high-efficiency Gaussian key reconciliation with efficiency higher than 95% for signal-to-noise ratios above 1. Our demonstrated method can be readily applied in continuous variable QKD.

Japanese Journal of Applied Physics•Mar 13, 2017•32 citations

Non-Gaussian Reconciliation for Continuous-Variable Quantum Key Distribution

Xiangyu Wang, Menghao Xu, Yin Zhao +3 more

Non-Gaussian modulation can improve the performance of continuous-variable quantum key distribution (CV QKD). For Gaussian-modulated coherent-state CV QKD, photon subtraction can realize non-Gaussian modulation, which can be equivalently implemented by non-Gaussian postselection. However, non-Gaussian reconciliation has not been deeply researched, which is one of the key technologies in CV QKD. In this paper, we propose a non-Gaussian reconciliation method to obtain identical keys from non-Gaussian data. Multidimensional reconciliation and multiedge-type low-density parity-check codes (MET LDPC) are used in a non-Gaussian reconciliation scheme, where the layered belief propagation decoding algorithm of MET LDPC codes is used to reduce the decoding complexity. Furthermore, we compare the error-correction performance of Gaussian data and non-Gaussian data. The results show that the error-correction performance of non-Gaussian data is better than Gaussian data, where the frame error rate can be reduced by 50 % for code rate 0.1 at SNR of 0.1554 and the average iteration number can be reduced by 25 %.

arXiv:2305.01963•Physical Review Applied•May 25, 2023•20 citations

Low-Dimensional Reconciliation for Continuous-Variable Quantum Key Distribution

László Gyöngyösi, Sándor Imre

We propose an efficient logical layer-based reconciliation method for continuous-variable quantum key distribution (CVQKD) to extract binary information from correlated Gaussian variables. We demonstrate that by operating on the raw-data level, the noise of the quantum channel can be corrected in the low-dimensional (scalar) space, and the reconciliation can be extended to arbitrary dimensions. The CVQKD systems allow an unconditionally secret communication over standard telecommunication networks. To exploit the real potential of CVQKD a robust reconciliation technique is needed. It is currently unavailable, which makes it impossible to reach the real performance of the CVQKD protocols. The reconciliation is a post-processing step separated from the transmission of quantum states, which is aimed to derive the secret key from the raw data. The reconciliation process of correlated Gaussian variables is a complex problem that requires either tomography in the physical layer that is intractable in a practical scenario, or high-cost calculations in the multidimensional spherical space with strict dimensional limitations. To avoid these issues, we define the low-dimensional reconciliation. We prove that the error probability of one-dimensional reconciliation is zero in any practical CVQKD scenario, and provides unconditional security. The results allow for significantly improving the currently available key rates and transmission distances of CVQKD.

arXiv:1308.1391•Applied Sciences•Jan 9, 2018•0 citations
The party Alice in a cryptograph system transmits coherent quantum signals to the party Bob,obtaining a series of correlated continuous Gaussian variables.The process to distill a binary key out of the correlated Gaussian variables that they share is called continuous-variable quantum key distribution(CVQKD).Reconciliation in CVQKD,i.e.,to correct differences between the correlated variables,is the key issue discussed in the paper.Based on both sliced error correction(SEC) protocol and multilevel coding/multistage decoding(MLC/MSD),reconciliation is implemented by LDPC code-based Slepian-Wolf CODEC.According to the proposed multilevel Tanner graph which depicts message transition of information,multistage iterative intrinsic and extrinsic information belief-propagation(LLR-BP) update formulae are derived.Three decoding modes of MSD are compared experimentally in convergence and performance.Simulation results show that the proposed algorithm can reconcile reliably 10000 continuous quantum variables with efficiency of 92.3% when SNR of the channel is above 2.5 dB.
Two legitimate users of an encryption system,Alice and Bob,want to acquire the key from the related Gaussian continuous variables X and Y transferred through a quantum channel,by exchanging parts of information through an ideal public authorized channel,and they get consistent binary keys from the inconsistent X and Y.This process is referred to reconciliation.This paper builds a reconciliation scheme for continuous-variables quantum key distribution using Turbo codes as the primitive code,on the basis of Sliced Error Correction(SEC) and Multi Level coding/Multi Stage Decoding(MLC/MSD).Parity bits of Turbo code are employed as the redundant information in the Slepian-Wolf encoding and decoding scheme.The simulation results show that the reconciliation convergences when the SNR is 7dB above whilst the block size is 20000.
Based on the Multilevel Codes/Multistage Decoding system,we achieved the reverse reconciliation for continuous variable quantum key distribution.Firstly,we show how to select the optimal quantization interval by maximizing the mutual information between the communicating parties.Then the optimal rate of each equivalent channel is calculated at the SNR level of 4 dB.The low-density parity check(LDPC) code is chosen as the channel codes,and the reverse reconciliation utilize a side-information based LDPC iterative decoding algorithm.
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.
Abstract Quantum key distribution (QKD) is the most mature application of quantum information technology. Information reconciliation is a crucial step in QKD and significantly affects the final secret key rates shared between two legitimate parties. We analyze and compare various construction methods of low-density parity-check (LDPC) codes and design high-performance irregular LDPC codes with a block length of 10 6 . Starting from these good codes and exploiting the slice reconciliation technique based on multilevel coding and multistage decoding, we realize high-efficiency Gaussian key reconciliation with efficiency higher than 95% for signal-to-noise ratios above 1. Our demonstrated method can be readily applied in continuous variable QKD.
Non-Gaussian modulation can improve the performance of continuous-variable quantum key distribution (CV QKD). For Gaussian-modulated coherent-state CV QKD, photon subtraction can realize non-Gaussian modulation, which can be equivalently implemented by non-Gaussian postselection. However, non-Gaussian reconciliation has not been deeply researched, which is one of the key technologies in CV QKD. In this paper, we propose a non-Gaussian reconciliation method to obtain identical keys from non-Gaussian data. Multidimensional reconciliation and multiedge-type low-density parity-check codes (MET LDPC) are used in a non-Gaussian reconciliation scheme, where the layered belief propagation decoding algorithm of MET LDPC codes is used to reduce the decoding complexity. Furthermore, we compare the error-correction performance of Gaussian data and non-Gaussian data. The results show that the error-correction performance of non-Gaussian data is better than Gaussian data, where the frame error rate can be reduced by 50 % for code rate 0.1 at SNR of 0.1554 and the average iteration number can be reduced by 25 %.
We propose an efficient logical layer-based reconciliation method for continuous-variable quantum key distribution (CVQKD) to extract binary information from correlated Gaussian variables. We demonstrate that by operating on the raw-data level, the noise of the quantum channel can be corrected in the low-dimensional (scalar) space, and the reconciliation can be extended to arbitrary dimensions. The CVQKD systems allow an unconditionally secret communication over standard telecommunication networks. To exploit the real potential of CVQKD a robust reconciliation technique is needed. It is currently unavailable, which makes it impossible to reach the real performance of the CVQKD protocols. The reconciliation is a post-processing step separated from the transmission of quantum states, which is aimed to derive the secret key from the raw data. The reconciliation process of correlated Gaussian variables is a complex problem that requires either tomography in the physical layer that is intractable in a practical scenario, or high-cost calculations in the multidimensional spherical space with strict dimensional limitations. To avoid these issues, we define the low-dimensional reconciliation. We prove that the error probability of one-dimensional reconciliation is zero in any practical CVQKD scenario, and provides unconditional security. The results allow for significantly improving the currently available key rates and transmission distances of CVQKD.