Continuous-Variable Quantum Key Distribution with Rateless Reconciliation Protocol

Chao Zhou, Xiangyu Wang, Yichen Zhang, Zhiguo Zhang, Song Yu, and Hong Guo

Phys. Rev. Applied 12, 054013 – Published 6 November 2019

Abstract

Information reconciliation is crucial for continuous-variable quantum key distribution (CV QKD) because its performance affects the secret key rate and maximal secure transmission distance. Fixed-rate error-correction codes limit the potential applications of the CV QKD because of the difficulty of optimizing such codes for different low SNRs. In this Paper, we propose a rateless reconciliation protocol combined multidimensional scheme with Raptor codes that not only maintains the rateless property but also achieves high efficiency in different SNRs using just one degree distribution. It significantly decreases the complexity of optimization and increases the robustness of the system. Using this protocol, the CV QKD system can operate with the optimal modulation variance, which maximizes the secret key rate. Simulation results show that the proposed protocol can achieve reconciliation efficiency of more than 95% within the range of SNR from $- 20$ to 0 dB. It also shows that we can obtain a high secret key rate at arbitrary distances in a certain range and achieve a secret key rate of about $5 \times 10^{- 4}$ bits/pulse at a maximum distance of 132 km (corresponding SNR is $- 20$ dB) that is higher than previous works. The proposed protocol can maintain highly efficient key extraction under the wide range of SNRs and paves the way toward the practical application of CV QKD systems in flexible scenarios.

Received 1 August 2019
Revised 16 October 2019

DOI:https://doi.org/10.1103/PhysRevApplied.12.054013

Physics Subject Headings (PhySH)

Photonics Quantum communication Quantum cryptography Quantum information processing with continuous variables Quantum networks Quantum optics

Quantum Information, Science & Technology

Authors & Affiliations

Chao Zhou¹, Xiangyu Wang¹, Yichen Zhang ^1,*, Zhiguo Zhang¹, Song Yu¹, and Hong Guo^2,†

¹State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China
²State Key Laboratory of Advanced Optical Communication, Systems and Networks, Department of Electronics, and Center for Quantum Information Technology, Peking University, Beijing 100871, China

^*zhangyc@bupt.edu.cn
^†hongguo@pku.edu.cn

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Vol. 12, Iss. 5 — November 2019

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Images

Figure 1
Factor graph for a Raptor code. $U_{k}$ denotes the initial $k$ bits. $V_{k'}$ denotes $k'$ input bits of $C$ . $C_{n}$ denotes the output $n$ bits. The nodes in the dashed border are redundancy nodes generated by precoding.
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Figure 2
Schematic diagram of rateless reconciliation protocol. $x$ and $y$ are two correlated Gaussian sequences. $x'$ and $y'$ represent the normalized sequences. $M (y', c')$ represents the mapping function sent from Bob to Alice. $u$ denotes the initial sequence generated by QRNG. $c$ is the Raptor encoding result of $u$ . $e$ is the sequence before decoding and $u'$ is the decoding result that is equal to $u$ when the decoding is successful. $r$ denotes the additional check codes. QRNG, quantum random-number generator.
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Figure 3
Reconciliation efficiencies under different SNRs. The red line segment represents the efficiency based on the rateless reconciliation protocol in this Paper with degree distribution adaptive (DD-adaptive) method. From left to right, dotted lines represent efficiency performances based on degree distribution $Ω_{1} (x)$ , $Ω_{2} (x)$ , $Ω_{3} (x)$ , and $Ω_{4} (x)$ , respectively. Other works, including quasicyclic (QC) MET LDPC codes [36], MET LDPC codes [38], spatially coupled (SC) LDPC codes [59], and polar codes [60] are also shown here.
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Figure 4
Optimal modulation variance vs distance and the corresponding SNR. The top right-hand corner shows enlargement from 34 to 124 km. The parameters of our CV QKD system are as follows: $ξ = 0.01$ , $η = 0.6$ , $α = 0.2 dB / km$ , $β = 95.6 %$ , and $ν_{el} = 0.015$ .
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Figure 5
Secret key rate with different modulation variances vs distance. The blue solid line is the secret key rate for optimal modulation variance and the orange solid line is the corresponding optimal modulation variance. The blue dotted line is the secret key rate for the modulation variance adjusted in real time according to the target $SNR = 0.075$ and the orange dotted line is the corresponding modulation variance. Neither set of data considers system overhead. Other parameters are as follows: $ξ = 0.01$ , $η = 0.6$ , $α = 0.2 dB / km$ , $β = 95.6 %$ , and $ν_{el} = 0.015$ .
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Figure 6
Finite-size secret key rate with 5-MHz repetition rate vs distance. The triangle points, five-pointed star, rhombus point, and six-pointed star correspond to our simulation results. Solid lines are asymptotic theoretical key rates. The first three lines from left to right correspond to block lengths of $N = 10^{10}, 10^{11}, 10^{12}$ , respectively, and their reconciliation efficiency $β = 0.95$ . The other solid lines represent the finite-size ( $10^{12}$ ) theoretical key rates with different efficiencies. The modulation variance $V_{A}$ is always kept at the optimal value, $β$ refers to the result based on rateless reconciliation protocol in Fig. 3. The orange dots are the secret key rates obtained from the state-of-the-art experiment [13, 61, 62, 63]. Green block points are the secret key rates obtained from the state-of-the-art field test [34, 64, 65, 66]. Other parameters in our results are as follows: $ξ = 0.01$ , $η = 0.6$ , $α = 0.2 dB / km$ , and $ν_{el} = 0.015$ .
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