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空间信道连续变量量子密钥分发协议(continuous-variable quantum key distribution, CV-QKD)工作在光学衍射极限、通信距离极限、光电探测极限条件下, 协议参数(如调制方差$ {V}_{\mathrm{A}} $)的优化选择会影响协议的可行性. 而低轨卫星和地面站始终处于高速相对运动中, 可视窗口时间有限且在轨计算资源受限, 传统优化算法难以满足空间信道快速动态变化的实时优化需求. 本文提出了空间信道高斯调制CV-QKD的Unet网络参数预测优化方法, 搭建空间CV-QKD链路仿真平台, 改变轨道高度、天顶角等组合参数生成126575组训练数据集, 利用Unet网络的对称结构和特征融合能力实现近实时地预测调制方差$ {V}_{\mathrm{A}} $. 仿真结果表明Unet网络在6328组跨轨道高度(510—710 km)和过量噪声水平(0.01—0.03)的测试数据中可以达到99.25%—99.41%的预测准确率, 同时相较于局部搜索算法14754 s的基准耗时, Unet将推理时间缩短至1.08 s (加速比达1.48 × 106), 为后续空间信道CV-QKD实验的参数实时优化提供了理论支撑.
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关键词:
- 连续变量量子密钥分发 /
- 参数优化 /
- 机器学习
Continuous-variable quantum key distribution (CV-QKD) has made significant progress in the field of quantum communication, operating under strict conditions such as optical diffraction limit, maximum communication distance, and photoelectric detection limit. The optimization of protocol parameters, particularly the modulation variance ($ {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. [1] 罗一振, 马洛嘉, 孙铭烁, 等 2024 物理学报 73 240302
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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
Fig. 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
Fig. 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
Fig. 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}}} $对比
Fig. 4. Comparison of predictions between the Unet model and traditional local search algorithms.
图 5 Unet网络与局部搜索算法预测结果一致性分析
Fig. 5. Consistency analysis of prediction results between the Unet network and local search algorithms.
图 6 不同过量噪声和轨道高度下, 不同优化方式得到的$ {V}_{\mathrm{A}} $值随通信时间的变化
Fig. 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
Fig. 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° 
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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/s Test data Local search 0.01—0.03 400—800 6328 99.41 14754.3 Test data Unet 0.01—0.03 400—800 6328 0.16 Test orbit1 Local search 0.01, 0.02, 0.03 510 446 99.36 1031.4 Test orbit1 Unet 0.01, 0.02, 0.03 510 446 0.0113 Test orbit2 Local search 0.01, 0.02, 0.03 610 518 99.25 1185.5 Test orbit2 Unet 0.01, 0.02, 0.03 610 518 0.0131 Test orbit3 Local search 0.01, 0.02, 0.03 710 582 99.28 1330.9 Test orbit3 Unet 0.01, 0.02, 0.03 710 582 0.0147
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[1] 罗一振, 马洛嘉, 孙铭烁, 等 2024 物理学报 73 240302
Google Scholar
Luo Y Z, Ma L J, Sun M S, et al. 2024 Acta Phys. Sin. 73 240302
Google Scholar
[2] Liao S K, Cai W Q, Liu W Y, et al. 2017 Nature 549 43
Google Scholar
[3] Yin J, Li Y H, Liao S K, et al. 2020 Nature 582 501
Google Scholar
[4] Ren J G, Xu P, Yong H L, et al. 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 [quant-ph]
[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
Google Scholar
[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
Google Scholar
Yin X H, Wang Y C, Li D Y 2021 J. Software 32 519
Google Scholar
[17] 陈宇杰, 程锦, 孙新, 刘胜豪, 张一鸣 2025 中国激光 52 330
Google Scholar
Chen Y J, Cheng J, Sun X, Liu S H, Zhang Y M 2025 Chin. J. Lasers 52 330
Google Scholar
[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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