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在光纤信道中, 连续变量量子密钥分发协议(continuous-variable quantum key distribution, CV-QKD)已经展现出获得更高安全码率的能力, 但是CV-QKD协议可容忍的信道衰减相对较低, 空间衍射、大气折射、信号衰减和湍流等实际因素都会影响空间信道中CV-QKD协议的可行性. 本文研究了实际空间信道环境下离散调制CV-QKD协议的可行性, 分析了空间衍射和大气衰减、湍流信道退化模型对于空间信道离散调制CV-QKD协议的影响, 讨论了卫星轨道高度、天顶角、接收器孔径、束腰尺寸和过量噪声等实际参数对空间离散调制CV-QKD的密钥生成率影响, 搭建了星地动态运动场景仿真分析了实际环境下空间信道离散调制CV-QKD协议的可行性, 仿真结果可为空间信道离散调制CV-QKD实验的设计和优化提供参考.
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关键词:
- 空间信道 /
- 连续变量量子密钥分发 /
- 星地下行链路 /
- 离散调制
Continuous variable quantum key distribution (CV-QKD) has emerged as a promising candidate for quantum-secure communication due to its experimentally demonstrated high key rates in fiber-optic channels. However, the feasibility of discrete modulation CV-QKD in satellite-to-ground downlinks remains an open question due to practical challenges such as high transmission loss, limited communication windows, and atmospheric turbulence. In this work, a comprehensive framework is proposed to evaluate the feasibility of discrete modulation CV-QKD by integrating orbital dynamics and atmospheric channel models, and to comprehensively analyze the influence of the parameter space on free-space discrete modulation CV-QKD. To achieve this, a free-space CV-QKD simulation platform is employed, which calculates the elevation angle and transmission distance based on precise orbital models, thereby providing a more practical assessment of the key rate for discrete modulation CV-QKD. Simulation results verify the feasibility and practicality of discrete modulation CV-QKD in satellite-based quantum communication systems. Furthermore, the critical factors influencing the key rate performance are identified, and parameter optimization strategies are proposed, providing theoretical support for realizing the future satellite-to-ground discrete modulation CV-QKD.
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Keywords:
- space channel /
- continuous-variable quantum key distribution /
- satellite underground links /
- discrete modulation
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图 1 QPSK协议的空间信道制备测量模型和星座示意图(PM, 相位调制器; EPC, 电极化控制器; LO, 本地振荡器; BS, 分束器; PD, 光电探测器)
Fig. 1. Measurement model and constellation schematic of spatial channel preparation for QPSK protocols. PM, phase modulator; EPC, electrical polarization controller; LO, local oscillator; BS, beam splitter; PD, photodetector
图 2 星地量子密钥分发场景图 (a)卫星动态通信轨道图; (b)光的传输遍历过程图.
Fig. 2. Scenario graph of star-earth quantum key distribution: (a) Satellite dynamic communications orbit graph; (b) graph of the light transmission traversal process.
图 3 卫星与地面站之间的距离、天顶角以及传输损耗随轨道运动变化图 (a)距离变化; (b)天顶角和传输损耗变化
Fig. 3. Graphs of distance, zenith angle and transmission loss between the satellite and the ground station as a function of orbital motion: (a) Change in distance; (b) change in zenith angle and transmission loss.
图 4 传输损耗及密钥率与轨道高度和天顶角的关系图 (a)传输损耗与轨道高度和天顶角的关系; (b)密钥率与轨道高度和天顶角的关系
Fig. 4. Graph of transmission loss and key rate versus orbital altitude and zenith angle: (a) Transmission loss versus orbit height and zenith angle; (b) key rate versus orbital altitude and zenith angle.
图 5 传输损耗及密钥率与光束腰尺寸和接收孔径的关系图 (a)传输损耗与光束腰尺寸和接收孔径的关系; (b)密钥率与光束腰尺寸和接收孔径的关系
Fig. 5. Graph of transmission loss and key rate versus beam waist size and acceptance aperture: (a) Transmission loss versus beam waist size and acceptance aperture; (b) key rate as a function of beam waist size and acceptance aperture.
图 6 DM CV-QKD在不同过量噪声下的密钥率
Fig. 6. Key rate of DM CV-QKD with different additional noises.
图 7 DM CV-QKD在动态轨道下的最佳幅值和密钥率 (a)最佳幅值; (b)密钥率
Fig. 7. Optimal magnitude and key rate for DM CV-QKD in dynamic orbit: (a) Optimal amplitude; (b) key rate.
表 1 用于模拟墨子号-丽江站的参数
Table 1. Parameters used to simulate the Mercury-Lijiang station
参数 参考值 光束尺寸ω0 20 cm 接收孔径αR 0.9 m 探测效率$ {\tau _{{\text{eff}}}} $ 0.4 天顶传输效率$ {\tau _{{\text{zen}}}} $ 0.90 指向误差$ {\theta _{\text{p}}} $ 1 μrad 
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表 2 DM CV-QKD系统参数设置
Table 2. DM CV-QKD System Parameter Setting
参数 参考值 波长λ 1550 nm 调制幅度α 0.6 后处理值Δ 0 过量噪声$ {\xi _{{\text{tot}}}} $ 0.01 光子截止数Nc 12
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表 3 GM CV-QKD系统参数设置
Table 3. GM CV-QKD System Parameter Setting
参数 参考值 制备方差V 4 电子噪声$ {\xi _{{\text{el}}}} $ 0.1 反向调和效率β 0.95 过量噪声$ \xi $ 0.02
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