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Continuous-variable quantum key distribution (CV-QKD) has made significant progress in the field of quantum communication, operating under strict conditions such as optical diffraction limit, maximum communication distance, and photoelectric detection limit. The optimization of protocol parameters, particularly the modulation variance ($ {V}_{\mathrm{A}} $), is crucial for the feasibility of CV-QKD. However, in space-to-ground CV-QKD scenarios, the high-speed relative motion between low-earth-orbit satellites and ground stations, coupled with limited on-board computing resources, poses challenges for traditional optimization algorithms to meet the real-time demands of rapidly changing space channels. To cope with these challenges, a novel method of optimizing Gaussian-modulation CV-QKD in space channels using a Unet-based approach is proposed in this work. A comprehensive simulation platform for CV-QKD links, generating a substantial training dataset of 126575 samples by changing parameters such as orbital height and zenith angle, is developed in this work. The Unet network, renowned for its symmetric architecture and powerful feature fusion capabilities, is utilized to achieve near-real-time prediction of modulation variance. Our simulation results demonstrate the effectiveness of the proposed method, with the Unet network achieving a remarkable prediction accuracy of 99.25%—99.41% on 6328 datasets, orbital heights between 510 and 710 km, and excess noise levels between 0.01 and 0.03. Compared with the local search algorithm, which takes 14754 s, the Unet-based approach significantly reduces the inference time to just 1.08 s, representing a speed-up ratio of 1.48 × 106. These findings provide a solid theoretical foundation for optimizing real-time parameters in future space-channel CV-QKD experiments, and have made significant progress in the field of quantum communication. The proposed method not only enhances the efficiency of parameter optimization but also ensures the security and reliability of CV-QKD in dynamic space environments. -
图 1 基于Unet网络的自由空间高斯调制CV-QKD参数优化示意图
Figure 1. Schematic diagram of parameter optimization for free-space Gaussian-modulated CV-QKD based on a Unet network.
图 2 基于Unet网络的轻量化网络结构流程
Figure 2. Schematic of the lightweight network architecture based on a Unet network.
图 3 基于Unet网络的训练和验证损失曲线
Figure 3. Training and validation loss curves based on a Unet network.
图 4 Unet模型和传统的局部搜索算法预测$ {V}_{{\mathrm{A}}} $对比
Figure 4. Comparison of predictions between the Unet model and traditional local search algorithms.
图 5 Unet网络与局部搜索算法预测结果一致性分析
Figure 5. Consistency analysis of prediction results between the Unet network and local search algorithms.
图 6 不同过量噪声和轨道高度下不同优化方式得到的$ {V}_{\mathrm{A}} $值随通信时间的变化
Figure 6. Curves of $ {V}_{\mathrm{A}} $ values over communication time under different optimization methods for various excess noise levels and orbital heights.
图 7 不同轨道高度下, 不同调制方差$ {V}_{{\mathrm{A}}} $优化方法对密钥率生成的影响
Figure 7. Influences of different $ {V}_{{\mathrm{A}}} $ optimization methods on key rate generation under various orbital heights.
表 1 CelesTrak提供的两行轨道根数(TLE)数据
Table 1. Two-line element set (TLE) data from CelesTrak.
参数 描述 数值 历元时间 数据发布日期 16354.569 轨道倾角 轨道平面与赤道平面的夹角 97.3698° 升交点赤经 轨道与赤道交点的经度 268.1064° 偏心率 轨道椭圆程度 0.0013349 近地点幅角 升交点与近地点之间的夹角 175.8929° 平近点角 卫星在历元时刻的轨道位置 309.019° 历元时间 数据发布日期 16354.569 
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表 2 不同测试集在不同网络中的表现
Table 2. Performance of different test sets across various networks.
Set Method $ \xi /\mathrm{S}. \mathrm{N}. \mathrm{U} $ H/km Size Rate
/%Times
/sTest
datalocal
search0.01–0.03 400–800 6328 99.41 14754.3 Test
dataUnet 0.01–0.03 400–800 6328 0.16 Test
orbit1local
search0.01, 0.02,
0.03510 446 99.36 1031.4 Test
orbit1Unet 0.01, 0.02,
0.03510 446 0.0113 Test
orbit2local
search0.01, 0.02,
0.03610 518 99.25 1185.5 Test
orbit2Unet 0.01, 0.02,
0.03610 518 0.0131 Test
orbit3local
search0.01, 0.02,
0.03710 582 99.28 1330.9 Test
orbit3Unet 0.01, 0.02,
0.03710 582 0.0147
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[1] 罗一振, 马洛嘉, 孙铭烁 2024 物理学报 73 240301
Luo Y Z, Ma L J, Sun M S 2024 Acta Phys. Sin. 73 240301
[2] Liao S K, Cai W Q, Liu W Y, Zhang K, Li J, Ren J G, Yin J, Shen Q, Cao Y, Li Z P, Wu F C, Li W Q, Liu S L, Ren J G, Peng C Z, Chen X W, Pan J W 2017 Nature 549 43
Google Scholar
[3] Yin J, Li Y H, Liao S K, Yang M, Cao Y, Zhang L, Ren J G, Cai W Q, Liu W Y, Li S L, Shu R, Huang Y M, Deng L, Li L, Zhang Q, Liu N L, Chen Y A, Lu C Y, Wang X B, Peng C Z, Pan J W 2020 Nature 582 501
Google Scholar
[4] Ren J G, Xu P, Yong H L, Zhang L, Liao S K, Yin J, Liu W Y, Cai W Q, Yang M, Li L, Yang K X, Han X, Yao Y Q, Li J, Wu H Y, Wan S L, Liu L, Liu D Q, Kuang Y W, He Z P, Shang P, Guo C, Zheng K H, Tian K, Zhu Z C, Liu N L, Lu C Y, Shu R, Chen Y A, Peng C Z, Wang X B, Pan J W 2017 Nature 549 70
Google Scholar
[5] Dubey U, Bhole P, Dutta A, Goyal S K, Behera B K, Panigrahi P K 2023 arXiv 2309.13417
[6] Harney C, Fletcher A I, Pirandola S 2022 Phys. Rev. Appl. 18 014012
Google Scholar
[7] Long N K, Malaney R, Grant K J 2023 Information 14 553
Google Scholar
[8] Zhou Z C, Guo Y 2024 Electronics 13 1410
Google Scholar
[9] Wang W, Lo H K 2019 Phys. Rev. A 100 062334
Google Scholar
[10] Jin D, Guo Y, Wang Y, Li Y B, Wang T Y 2021 Phys. Rev. A 104 012616
Google Scholar
[11] Long N K, Malaney R, Grant K J 2024 Proc. SPIE 13106 1310602
[12] Liu Z P, Zhou M G, Liu W B, Wang P, Liu J Y, Guo Y 2022 Opt. Express 30 15024
Google Scholar
[13] Mao Y, Huang W, Zhong H, Liao Q, Zhang S L, Guo Y 2020 New J. Phys. 22 083073
Google Scholar
[14] Liao Q, Xiao G, Zhong H, Guo Y, Huang D 2020 New J. Phys. 22 083086
Google Scholar
[15] Liu W Q, Huang P, Peng J Y, Fan J P, Zeng G H 2018 Phys. Rev. A 97 022316
Google Scholar
[16] 殷晓航, 王永才, 李德英 2021 软件学报 32 519
Yin X H, Wang Y C, Li D Y 2021 J. Software 32 519
[17] 陈宇杰, 程锦, 孙新, 刘胜豪, 张一鸣 2025 中国激光 52 330
Chen Y J, Cheng J, Sun X, Liu S H, Zhang Y M 2025 Chin. J. Lasers 52 330
[18] Hornik K, Stinchcombe M, White H 1989 Neural Networks 2 359
Google Scholar
[19] Liao S K, Lin J, Ren J G, Liu C, Liang H, Yin J, Cao Y, Wu F C, Li S L, Li H, Shu R, Xue G, Li B, Shen Q, Jiang L, Yang L, Wang Z, You L X, Wang Z, Pan J W 2017 Chin. Phys. Lett. 34 090302
Google Scholar
[20] Pirandola S 2021 Phys. Rev. Research 3 023130
Google Scholar
[21] Weedbrook C, Lance A M, Bowen W P, Symul T, Ralph T C, Lam P K 2004 Phys. Rev. Lett. 93 170504
Google Scholar
[22] Katoch S, Chauhan S S, Kumar V 2021 Multimedia Tools Appl. 80 8091
Google Scholar
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