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源于量子内禀随机性的量子随机数发生器(quantum random number generator, QRNG)提供了安全性信息论可证的真随机数. 本文提出一种融合实时相空间监测与熵评估的二重并行连续变量QRNG方案, 通过动态阈值监测机制与自适应后处理矩阵规模调整技术, 同步提升QRNG安全性与生成效率, 该方案创新性地将熵源状态追踪与随机数提取优化相结合. 实验上构建基于外差探测的真空态双边带模并行提取系统, 为高精度、高速全息重构量子态和四路并行提取量子随机数提供了充足的原始数据; 高动态范围、高分辨率、矩阵规模实时可调的硬件基Toeplitz-hash后处理协调了熵源状态追踪与随机数提取优化. 在保持17 Gbit/s以上高产率的同时可有效抵御边信道攻击, 通过了NIST SP 800-22, Diehard及TestU01标准测试. 本工作为解决QRNG实时熵源可信评估难题提供了技术路径, 且该方案集成度高、扩展性好, 为量子随机数发生器走向应用提供了一种切实可行的方案.
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关键词:
- 量子随机数 /
- 连续变量量子态 /
- 量子条件最小熵 /
- FPGA实时Toeplitz-hash后处理
Continuous-variable quantum random number generator (cv-QRNG) has attracted much attention due to its convenient state preparation and high measurement bandwidth. Chip-size integration of this type of QRNG is expectable because all components involved have been integrated on a single chip recently. Most of the existing schemes, including all existing commercial schemes, usually use a once-and-for-all approach to evaluate quantum entropy. In this work, we propose a double-level parallel cv-QRNG scheme that integrates real-time phase-space monitoring and entropy evaluation. By using dynamic threshold monitoring and self-adapting scaling of Toeplitz matrix, the security and generation rate of QRNG can be enhanced simultaneously. Experimentally, a parallel extraction system of vacuum state double quadratures and multiple sideband modes is constructed based on heterodyne, providing sufficient raw data for high-precision and high-speed tomography reconstruction of quantum entropy source and parallel extraction of QRNG. Based on the statistical analysis of data under long-term stable operation of the system, dynamic KLD-sensitive security threshold for statistical distribution of Husimi-Q function of the entropy source is established. When a weak chaotic field is injected to simulate a thermal state attack, the KLD value jumps and quickly deviates from the steady state baseline, manifesting a sensitive identification of the attack. It is worth pointing out that the threshold parameter can be dynamically optimized according to the security requirements of actual application scenarios. An FPGA-based real-time feedback Toeplitz-hash extractor employs a maximum matrix bit-width truncation method to dynamically adjust Toeplitz matrix parameters. This optimization reduces the maximum extraction ratio interval from 6% to 1.8%, with all intervals below 1% for extraction ratios ≤76%, significantly mitigating entropy losses caused by discrete adjustment of the Toeplitz matrix, and achieving a minimum extraction ratio of 16.9%. This flexibility enables the system to accurately control the response sensitivity of abnormal signals while maintaining the real-time generation of quantum random bits. Finally, real-time generation rate of 17.512 Gbit/s is attained with security parameters at the level of 10–50 and the generated random numbers passed NIST SP 800-22, Diehard, and TestU01 standard tests. This research provides a technical path for real-time assessment of entropy source security in QRNG. The proposed scheme has good integrability and scalability, presenting a feasible solution for QRNG to enter the application stage. -
Keywords:
- quantum random number /
- continuous variable quantum state /
- quantum conditioned min-entropy /
- FPGA based real-time Toeplitz-hash postprocessing
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图 1 基于外差探测的多路并行实时熵评估QRNG实验方案, 其中TC为温控源, CS为电流源, LD为半导体激光器, VOA为衰减器, OPC为光学偏振器, BS1为80∶20分束器, Laser为激光源, BS2为 90∶10分束器, 90°Hybrid为90°光混频器, OPM为功率计, BHD为光电探测器, PS为功分器, M为混频器, AWG为信号发生器, LPF为滤波器, ADC为模数转换器, FPGA为现场可编程门阵列, PC为上位机
Fig. 1. A multi-channel parallel real-time entropy evaluation QRNG experimental scheme based on heterodyne detection, where TC represents temperature-controlled source, CS represents current source, LD represents semiconductor laser, VOA represents attenuator, OPC represents optical polarizer, BS1 represents 80∶20 beam splitter, Laser represents laser source, BS2 represents 90∶10 beam splitter, 90° hybrid represents 90° optical mixer, OPM represents power meter, BHD represents photodetector, PS represents power divider, M represents mixer, AWG represents signal generator, LPF represents filter, ADC represents analog-to-digital converter, FPGA represents field programmable gate array, PC represents upper computer.
图 3 后处理与熵反馈模块示意图
Fig. 3. Schematic diagram of the post-processing and entropy feedback module.
图 5 (a) TestU01测试结果; (b) Diehard测试结果
Fig. 5. (a) Test results of TestU01; (b) test results of Diehard.
图 6 不同探测效率下层析精度变化曲面图 (a) η = 0.1; (b) η = 0.5; (c) η = 0.72; (d) η = 1
Fig. 6. Performance ratio surface plot for different detection efficiency: (a) η = 0.1; (b) η = 0.5; (c) η = 0.72; (d) η = 1.
图 7 不同探测效率下层析精度变化曲面图(考虑Arthurs-Kelly误差) (a) η = 0.1; (b) η = 0.5; (c) η = 0.72; (d) η = 1
Fig. 7. Performance ratio surface plot considering Arthurs-Kelly error with different detection efficiency: (a) η = 0.1; (b) η = 0.5; (c) η = 0.72; (d) η = 1.
图 8 不同效率下的性能比与光子数的关系
Fig. 8. Relationship between performance ratio and number of photons at different efficiencies.
图 9 信号方差随本振光功率的变化
Fig. 9. Relationship of signal variance with local oscillator optical power.
图 10 实验重构结果 (a) 不同本振功率下KLD随迭代次数的变化; (b) 迭代300次的Wigner分布; (c) 不同本振功率下KLD随截断值kc的变化图; (d) 截断值kc为4的Wigner分布; (e) HET中KLD随着本振功率变化; (f) HET重构的Husimi-Q分布
Fig. 10. Experimental reconstruction results: (a) The variation of KLD with the number of iterations at different local oscillator powers; (b) Wigner distribution with 300 iterations; (c) Variation of KLD with kc at different local oscillator powers; (d) Wigner distribution with a cut-off value of kc of 4; (e) KLD in HET with local oscillator power; (f) Husimi-Q distribution reconstructed by HET.
图 11 不同数据量下3种重构方法的KLD值
Fig. 11. The KLD value of the three reconstruction methods under different sample sizes.
图 12 (a) 热态攻击前后的Husimi-Q 分布, 其中网格化曲线对应真空态, 彩色直方图对应热态; (b) 热态攻击前后的KLD波动图
Fig. 12. (a) Husimi-Q distribution before and after a thermal attack, where gridded curve corresponds to vacuum state, color histogram corresponds to hot state; (b) KLD fluctuation plot before and after thermal attack.
图 13 最小熵与QSNR关系图
Fig. 13. Graph of minimum entropy versus quantum signal-to-noise ratio.
图 14 后处理矩阵调整流程示意图
Fig. 14. Schematic diagram of the post-processing matrix adjustment process.
图 16 (a) 矩阵步长为128时的后处理离散提取比例; (b) 矩阵步长为32时的后处理离散提取比例
Fig. 16. (a) Post-processing discrete extraction ratio at matrix step size of 128; (b) post-processing discrete extraction ratio at matrix step size of 32.
表 1 不同通道的关键参数
Table 1. Structural parameters of capillary of different kind of fluid.
通道 条件最小熵
/(16 bit)矩阵规模
m × n后处理提
取比/%实时生
成速率
/(Gbit·s–1)X (300 MHz) 11.79 1729×2496 69.27 4.4334 P (300 MHz) 11.71 1729×2496 69.27 4.4334 X (800 MHz) 11.54 1729×2560 67.54 4.3226 P (800 MHz) 11.45 1729×2560 67.54 4.3226 
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