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Acta Sinica Quantum Optica

Reverse Reconciliation for Continuous Variable Quantum Key Distribution

Yongmin Li

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

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.

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Physical Review A•Mar 9, 2021•24 citations
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.
We have demonstrated a reverse reconciliation of a continuous-variable quantum key distribution system with efficient low-density parity check codes. A standard coded modulation technique, called Multi Level Coding/ Multistage Decoding scheme, is used to optimize the reconciliation. Via a numerical simulation, we get the results that efficiency of the reconciliation algorithm reaches 0.89 while the final secure key distribution rate of the whole system is more than 2.2 kbits/s over 20 km of single-mode optical fiber.
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.
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.
An information reconciliation method for continuous-variable quantum key distribution with Gaussian modulation that is based on non-binary low-density parity-check (LDPC) codes is presented. Sets of regular and irregular LDPC codes with different code rates over the Galois fields GF(8)GF(8)GF(8), GF(16)GF(16)GF(16), GF(32)GF(32)GF(32), and GF(64)GF(64)GF(64) have been constructed. We have performed simulations to analyze the efficiency and the frame error rate using the sum-product algorithm. The proposed method achieves an efficiency between 0.940.940.94 and 0.980.980.98 if the signal-to-noise ratio is between 444 dB and 242424 dB.
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.
The well-known multidimensional reconciliation is a significant stage of a continuous-variable quantum key distribution (CVQKD) system, which uses ddd-dimensional rotations to build a virtual channel between authenticated parties, Alice and Bob. Generally, a block low-density parity-check code with a belief-propagation (BP) iterative decoding algorithm, which is optimized for an additive white Gaussian noise channel, is always used in multidimensional reconciliation for the CVQKD system. In this paper, we study the signal-to-noise ratio (SNR) of the virtual channel of multidimensional reconciliation in CVQKD and prove that the noise of the virtual channel follows the Student's ttt-distribution. Therefore, we propose a ttt-BP decoding algorithm, which can be better applied to multidimensional reconciliation. Simulation results show that the frame error rate (FER) with the proposed ttt-BP decoding algorithm is superior to that with the conventional BP decoding algorithm applied to multidimensional reconciliation. Subsequently, the FER improvement results in significant influence on reconciliation efficiency and secret key rate of the CVQKD system.