Practical security of wavelength-multiplexed decoy-state quantum key distribution

Liang-Yuan Zhao, Qian-Jun Wu, Hong-Kang Qiu, Jian-Lin Qian, and Zheng-Fu Han

Phys. Rev. A 103, 022429 – Published 26 February 2021

Abstract

Wavelength division multiplexing (WDM) of quantum key distribution (QKD) with classical optical channels has been proven to be feasible experimentally. In this paper, we will analyze the practical security of WDM-QKD theoretically. Specifically, we first establish the noise model of classical signals. Then, the influence of classical noises on the performance of decoy-state WDM-QKD is studied with a finite-key security analysis. For numerical simulations, the effect of classical noise-reduction methods for different experimental settings is given. The secret key rate and maximum transmission distance of WDM-QKD is simulated with various sent number of quantum pulses or transmitted power of classical signals. Furthermore, the performance of two kinds of decoy-state WDM-QKD is compared, which shows that the optimal decoy-state protocol for WDM-QKD is related to the sent number of quantum pulses. Since WDM-QKD is desired to reduce the cost of QKD networks and since experiments have already been carried out, our work can not only close the gap between theory and practice, but also be used to optimize the experimental parameters and improve its performance.

Received 23 March 2020
Accepted 13 January 2021

DOI:https://doi.org/10.1103/PhysRevA.103.022429

Physics Subject Headings (PhySH)

Quantum channels Quantum communication Quantum cryptography Quantum networks

Quantum Information, Science & Technology

Authors & Affiliations

Liang-Yuan Zhao^1,2,3,*, Qian-Jun Wu¹, Hong-Kang Qiu¹, Jian-Lin Qian², and Zheng-Fu Han³

¹Jiangsu Hengtong Qasky Quantum Information Research Institute Co., Ltd., Suzhou, Jiangsu 215200, China
²Jiangsu Hengtong Optic-Electric Co., Ltd., Suzhou, Jiangsu 215200, China
³Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei, Anhui 230026, China

^*zhaoly@htgd.com.cn

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Vol. 103, Iss. 2 — February 2021

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Images

Figure 1
Schematic of a general structure of WDM-QKD. ATT: optical attenuator; F: filter; Mux/Demux: wavelength division multiplexer or demultiplexer.
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Figure 2
Comparison of the detection rates of SRS noise and FWM noise. ${SRS}_{f}$ and ${SRS}_{b}$ denote the forward and backward SRS noises, respectively. The transmission power of the classical signals is $- 10$ dBm for (a) and (b), while it is increased to 0 dBm for (c) and (d). (a), (c) The bandwidth of filter $Δ λ = 35.23$ pm and the gate width of SPD $Δ τ_{D} = 100$ ps. (b), (d) The bandwidth of filter $Δ λ = 3.523$ pm and the gate width of SPD $Δ τ_{D} = 1$ ns.
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Figure 3
The relationships between the detection rates of SRS and FWM noises and the transmitted power of the classical signals with $L = 15$ km. ${SRS}_{f}$ and ${SRS}_{b}$ denote the forward and backward SRS noises respectively. The bandwidth of filter $Δ λ = 3.523$ pm and the gate width of SPD $Δ τ_{D} = 1$ ns.
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Figure 4
The relationships between the secret key rate and transmission distance for WDM-QKD with different finite resources. The transmitted power of classical signals is fixed to be $- 10$ dBm, and the other parameters used are listed in Table. 1. Note that co(two) denotes the two-decoy-state WDM-QKD with solid lines in the figure, and co(one) denotes the one-decoy-state WDM-QKD with dashed lines. The various transmitted numbers of quantum signals are distinguished by the data point symbols. For comparison, the performances of noncoexistent QKD with symbols inco(two) and inco(one) for the two-decoy-state protocols are also shown in the same figure.
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Figure 5
The relationships between the maximum secure distance and total sent number of quantum pulses for WDM-QKD with fixed classical signals transmission power. The maximum secure distance approaches the asymptotic case if $N \geq 10^{12}$ . The range of the minimum value of $N$ is about $10^{7}$ to $10^{8}$ to make the secret key rate positive. The various transmitted powers of classical signals are distinguished by the data point symbols. The meanings of co(two) with solid lines and co(one) with dashed lines are the same as in Fig. 4.
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Figure 6
The relationships between the maximum secure distance and transmitted power of classical signals for WDM-QKD with fixed sent number of quantum pulses. The various transmitted numbers of quantum signals are distinguished by the data point symbols. The meanings of co(two) with solid lines and co(one) with dashed lines are the same as in Figs. 4 and 5.
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