Real-time entropy source evaluated dual-parallel continuous variable quantum random number generator

GUO Xiaomin; WANG Qiqi; LUO Yue; SONG Zhijie; LI Zhengya; QU Yikun; GUO Yanqiang; XIAO Liantuan

doi:10.7498/aps.74.20250333

Abstract

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:

Authors and contacts

1.
Key Laboratory of Advanced Transducers and Intelligent Control System, Ministry of Education, Taiyuan University of Technology, Taiyuan 030024, China
2.
College of Physics and Optoelectronics, Taiyuan University of Technology, Taiyuan 030024, China

Corresponding author: GUO Yanqiang, guoyanqiang@tyut.edu.cn ; XIAO Liantuan, xlt@sxu.edu.cn

Funds: Project supported by the National Key Research and Development Program of China (Grant No. 2022YFA1404201), the National Natural Science Foundation of China (Grant Nos. 62475185, 62175176, U23A20380), and the Fundamental Research Program of Shanxi Province, China (Grant No. 202403021221034).

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References

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Cited By

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

Figure 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.

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图 2 真空态双分量散粒噪声功率谱图

Figure 2. Vacuum-state two-component shot noise power spectrum.

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图 3 后处理与熵反馈模块示意图

Figure 3. Schematic diagram of the post-processing and entropy feedback module.

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图 4 标准NIST统计套件测试结果

Figure 4. Standard NIST statistical suite test results.

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图 5 (a) TestU01测试结果; (b) Diehard测试结果

Figure 5. (a) Test results of TestU01; (b) test results of Diehard.

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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

Figure 6. Performance ratio surface plot for different detection efficiency: (a) η = 0.1; (b) η = 0.5; (c) η = 0.72; (d) η = 1.

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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

Figure 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.

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图 8 不同效率下的性能比与光子数的关系

Figure 8. Relationship between performance ratio and number of photons at different efficiencies.

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图 9 信号方差随本振光功率的变化

Figure 9. Relationship of signal variance with local oscillator optical power.

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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k_c的变化图; (d) 截断值k_c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

Figure 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 k_c at different local oscillator powers; (d) Wigner distribution with a cut-off value of k_c of 4; (e) KLD in HET with local oscillator power; (f) Husimi-Q distribution reconstructed by HET.

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图 11 不同数据量下3种重构方法的KLD值

Figure 11. The KLD value of the three reconstruction methods under different sample sizes.

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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

Figure 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.

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图 13 最小熵与QSNR关系图

Figure 13. Graph of minimum entropy versus quantum signal-to-noise ratio.

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图 14 后处理矩阵调整流程示意图

Figure 14. Schematic diagram of the post-processing matrix adjustment process.

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图 15 可变的矩阵规模硬件实现方法

Figure 15. Variable matrix size implementation.

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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

Figure 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.

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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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