Finite Key Optimization Analysis for Satellite-to-Ground Continuous-Variable Quantum Key Distribution

Yujie Chen; Jin Cheng; Xin Sun; Junjie Guo; Ao Liu; Peng Yin; Lanjian Chen; Chen Dong

doi:10.3788/CJL241102

Chinese Journal of Lasers, Volume. 52, Issue 6, 0612001(2025)

Finite Key Optimization Analysis for Satellite-to-Ground Continuous-Variable Quantum Key Distribution

Yujie Chen, Jin Cheng, Xin Sun, Junjie Guo, Ao Liu, Peng Yin, Lanjian Chen, and Chen Dong^*

Author Affiliations

College of Information and Communication, National University of DefenseTechnology, Wuhan 430033, Hubei , China

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Figures & Tables(11)

Fig. 1. Schematic diagram of PM model for no-switching GM CV-QKD

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Fig. 2. Satellite-to-ground quantum key distribution scenario diagram. (a) Satellite dynamic time-varying orbit model diagram; (b) illustration of effective atmospheric transmission distance of light

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Fig. 3. Graph of distance, zenith angle, and transmission loss between satellite and four ground stations versus orbit motion. (a) Distance; (b) zenith angle; (c) transmission loss

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Fig. 4. Key rate and total key amount per satellite pass versus preparation variance. (a) $I_{A B}$ , $χ_{B E}$ and key rate versus preparation variance; (b) relationship between total key amount per satellite pass and preparation variance under different reverse reconciliation efficiencies

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Fig. 5. Relation between key generation rate and preparation variance for free space CV-QKD and fiber CV-QKD under the same conditions

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Fig. 6. Variation of key rate with satellite movement for DV-QKD and GM CV-QKD protocols

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Fig. 7. Relationship between the total key amount, symbol transmission rate, total data volume N,and m/N. (a) Relationship between the total key amount and symbol transmission rate $f_{T X}$ ; (b) relationship between the total key amount and total data volume N and m/N

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Table 1. Parameters configuration for satellite and ground stations

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Table 1. Parameters configuration for satellite and ground stations

Parameter	Symbol	Value
Pointing error /μrad	$θ_{p}$	$1$
Beam divergence angle /μrad	$θ_{d}$	$10$
Detector electronic noise / $S . N . U .$	$v_{e l}$	$0.1$
Detection efficiency	$η$	$80 %$
Optical loss of the system / $d B$	$η_{e f f}$	$3.8$
Receiving telescope radius /m	a_R	$0.5$

Table 2. CV-QKD system parameter configuration
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Table 2. CV-QKD system parameter configuration
Parameter Symbol Value
Signal wavelength /nm $λ$ $1550$
Fixed excess noise / $S . N . U .$ $ε_{f i x}$ $0.01$
Backward coordination efficiency $β$ $0.95$
Preparation variance / $S . N . U .$ $V_{A}$ $4$

Table 3. Partial parameter settings for the simulation results in Fig. 6

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Table 3. Partial parameter settings for the simulation results in Fig. 6

Parameter name	Parameter setting
Parameter name	DV-QKD	CV-QKD
Signal wavelength /nm	$850$	$1550$
Fixed excess noise / $S . N . U .$		$0.032 ‒ 0.042$
Optical loss of the system /dB	$5.9$	$5.9$
Background light count rate	$3 \times 10^{- 6}$
Misalignment error	$15 %$
Error correction efficiency	$1.2$
Detection efficiency	50%	50%

Table 4. m_best/N under different total symbol counts
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Table 4. m_best/N under different total symbol counts
$N / G s y m b o l$ m_best /N Total data $/ (10^{8} b i t)$
1 0.4 1.38
2 0.3 4.05
3 0.3 7.27
4 0.25 10.82
5 0.25 14.63
6 0.25 18.61
$7$ 0.25 22.72
8 0.2 26.98
9 0.2 31.40
10 0.2 35.91

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Yujie Chen, Jin Cheng, Xin Sun, Junjie Guo, Ao Liu, Peng Yin, Lanjian Chen, Chen Dong. Finite Key Optimization Analysis for Satellite-to-Ground Continuous-Variable Quantum Key Distribution[J]. Chinese Journal of Lasers, 2025, 52(6): 0612001

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