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在实际的连续变量量子秘密共享系统中, 经不安全信道传输的本振光或因各种针对性攻击而受到安全威胁. 针对这个问题, 本文提出了一种本地本振连续变量量子秘密共享方案, 本振光在可信端本地生成而无需由各用户发送, 从而彻底堵住相关安全漏洞. 在此基础上, 利用卡尔曼滤波对各个参考相位分别进行最小均方误差估计, 在降低相位漂移估计误差的同时抑制相位测量噪声. 分别开发了涉及标量卡尔曼和矢量卡尔曼的相位补偿方法, 其中矢量卡尔曼一步完成补偿而无需额外处理相位慢漂移. 本文对滤波后系统的过噪声进行建模, 并推导了针对窃听者和不诚实用户的安全界限. 数值模拟结果表明, 与块平均相比, 所提方案在最大传输距离和最大支持用户数方面优势明显, 具有构建大规模量子通信网络的潜力.In a practical continuous-variable quantum secret sharing system, the local oscillator transmitted via an insecure channel may be subjected to security threats due to various targeted attacks. To solve this problem, this paper proposes a continuous-variable quantum secret sharing scheme with local intrinsic oscillator, in which the intrinsic oscillator is generated locally at the trusted end without being sent by each user, thus completely plugging the relevant security loopholes. The scheme consists of three stages: preparation, where users generate Gaussian-modulated coherent states and reference signals; measurement, where the dealer performs heterodyne detection by using the local intrinsic oscillator and reference phases; post-processing, which involves parameter estimation, phase compensation, and secure key extraction. On this basis, Kalman filter (KF) is utilized to estimate the minimum mean square error for each reference phase separately, reducing the phase drift estimation error and suppressing the phase measurement noise. Phase compensation methods for scalar KF and vector KF are developed respectively, where scalar KF requires additional block averaging for slow phase drift, while vector KF simultaneously models fast and slow drifts, enabling one-step compensation with minimized estimation errors. The excess noise of the filtered system including modulation noise, phase noise, photon leakage noise, and ADC quantization noise is modeled, with KF reducing phase measurement noise via dynamic gain optimization. Security bound against eavesdroppers and dishonest users is derived. Numerical simulations under practical parameters demonstrate significant improvements: vector KF achieves a maximum transmission distance of 82.6 km (vs. 67.3 km for block averaging) and supports 33 users (vs. 22), with excess noise reduced by 40% at 60 km. The scheme’s robustness is further validated under varying reference signal amplitudes, showing stable performance even at lower levels, minimizing interference with quantum signals. These results highlight that the proposed scheme has significant advantages in terms of maximum transmission distance and maximum number of supported users, and has the potential to build adaptive KF algorithms for dynamic user scenarios and quantum machine learning integration.
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Keywords:
- quantum secret sharing /
- continuous variable /
- local local oscillator /
- Kalman filter
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图 2 不同相位补偿方法下所提方案性能, 插图为相位漂移估计误差与相位测量误差的函数关系
Fig. 2. Performance of the proposed scheme with different phase compensation methods, and the subplot shows the phase drift estimation error as a function of the phase measurement error.
图 3 不同参考信号幅值下所提方案与块平均方案性能; 小图为传输距离60 km时系统过噪声与$ {\left| {{\alpha _{\text{R}}}} \right|^2} $的函数关系
Fig. 3. Performance of the proposed scheme and block averaging for different reference signal amplitudes, and the small figure shows the excess noise as a function of $ {\left| {{\alpha _{\text{R}}}} \right|^2} $ at a transmission distance of 60 km.
图 4 不同(n, n)阈值下所提方案和块平均方案性能
Fig. 4. Performance of the proposed scheme and block averaging for different (n, n) thresholds.
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