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Acta Physica Sinica

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

Xiaomin Guo, Qiqi WANG, Yue Luo, Zhijie SONG, Zhonglin Li, Yikun QU, Yanqiang Guo, Liantuan Xiao

Published Jan 1, 2025• 3 citations
Publisher

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.

DOI
10.7498/aps.74.20250333

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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.
Abstract We present a high-speed continuous-variable quantum random number generator (QRNG) based on heterodyne detection of vacuum fluctuations. The scheme follows a source-device-independent security model in which the entropy originates from quantum measurement uncertainty and no model of the source is required; security depends only on the trusted measurement device and the calibrated discretization, and thus remains valid even under adversarial state preparation. The optical field is split by a 90 ∘ optical hybrid and measured by two balanced photodiodes to obtain both quadratures of the vacuum state simultaneously. The analog outputs are digitized using a dual-channel 12-bit analog-to-digital converter operating at a sampling rate of 3.2 GS s −1 per channel, and processed in real time by an field-programmable gate array (FPGA) implementing Toeplitz hashing for randomness extraction. The quantum-to-classical noise ratio was verified through calibrated power spectral density measurements and cross-checked in the time domain, confirming vacuum-noise dominance within the 1.6 GHz detection bandwidth. After extraction, the system achieves a sustained generation rate of R net = 33.92 Gbit s − 1 of uniformly distributed random bits, which pass all NIST and Dieharder statistical tests. The demonstrated platform provides a compact, FPGA-based realization of a practical heterodyne continuous-variable source-independent QRNG suitable for high-rate quantum communication and secure key distribution systems.
Continuous-variable quantum random number generators (CV-QRNGs) have promising application prospects thanks to their advantages such as high detection bandwidth, robustness of system, and integratability. In major CV-QRNGs, the generation of random numbers is based on homodyne detection and discretization of the quadrature fluctuations of the EM fields. Any defectiveness in physical realization may leak information correlated with the generated numbers and the maximal amount of randomness that can be extracted in presence of such side-information is evaluated by the so-called quantum conditional min-entropy. The parallel CV-QRNG overcomes the rate bottleneck of the previous serial type scheme. As a type of device-trusted QRNG, its security needs to be better guaranteed based on self-testing or monitoring that can be rigorously enforced. In this work, four sideband modes of vacuum state within 1.6 GHz detection bandwidth were extracted parallelly as the entropy source, and 16-bit analog-to-digital conversion in each channel was realized. Without making any ideal assumptions, the transfer function of the homodyne and quantization system was measured based on beat method to calibrate the evaluation of the min-entropy. Based on the rigorous entropy evaluation with a hash security parameter of εhash = 2−110, a real-time generation rate of 7.25 Gbps was finally achieved.
We present a high-speed continuous-variable quantum random number generator (QRNG) based on heterodyne detection of vacuum fluctuations. The scheme follows a source-device-independent (SDI) security model in which the entropy originates from quantum measurement uncertainty and no model of the source is required; security depends only on the trusted measurement device and the calibrated discretization, and thus remains valid even under adversarial state preparation. The optical field is split by a 90∘^\circ∘ optical hybrid and measured by two balanced photodiodes to obtain both quadratures of the vacuum state simultaneously. The analog outputs are digitized using a dual-channel 12-bit analog-to-digital converter operating at a sampling rate of 3.2 GS/s per channel, and processed in real time by an FPGA implementing Toeplitz hashing for randomness extraction. The quantum-to-classical noise ratio was verified through calibrated power spectral density measurements and cross-checked in the time domain, confirming vacuum-noise dominance within the 1.6 GHz detection bandwidth. After extraction, the system achieves a sustained generation rate of Rnet=33.92 Gbit/sR_{\rm net}= 33.92~\mathrm{Gbit/s}Rnet​=33.92 Gbit/s of uniformly distributed random bits, which pass all NIST and Dieharder statistical tests. The demonstrated platform provides a compact, FPGA-based realization of a practical heterodyne continuous-variable source-independent QRNG suitable for high-rate quantum communication and secure key distribution systems.
Quantum random number generators (QRNG) based on continuous variable (CV) quantum fluctuations offer great potential for their advantages in measurement bandwidth, stability and integrability. More importantly, it provides an efficient and extensible path for significant promotion of QRNG generation rate. During this process, real-time randomness extraction using information theoretically secure randomness extractors is vital, because it plays critical role in the limit of throughput rate and implementation cost of QRNGs. In this work, we investigate parallel and real-time realization of several Toeplitz-hashing extractors within one field-programmable gate array (FPGA) for parallel QRNG. Elaborate layout of Toeplitz matrixes and efficient utilization of hardware computing resource in the FPGA are emphatically studied. Logic source occupation for different scale and quantity of Toeplitz matrices is analyzed and two-layer parallel pipeline algorithm is delicately designed to fully exploit the parallel algorithm advantage and hardware source of the FPGA. This work finally achieves a real-time post-processing rate of QRNG above 8 Gbps. Matching up with integrated circuit for parallel extraction of multiple quantum sideband modes of vacuum state, our demonstration shows an important step towards chip-based parallel QRNG, which could effectively improve the practicality of CV QRNGs, including device trusted, device-independent, and semi-device-independent schemes.
The quantum random number generation exploits inherent randomness of quantum mechanical processes and measurements. The real-time generation rate of quantum random numbers is usually limited by electronic bandwidth and data processing rates. Here we use a multiplexing scheme to create a fast real-time quantum random number generator based on continuous variable vacuum fluctuations. Multiple sideband frequency modes of a quantum vacuum state within a homodyne detection bandwidth are concurrently extracted as the randomness source. Parallel postprocessing of raw data from three subentropy sources is realized in one field-programmable gate array (FPGA) based on Toeplitz-hashing extractors. A cumulative generation rate of 8.25 Gbps in real time is achieved. The system relies on optoelectronic components and circuits that could be integrated in a compact, economical package.
Secure communication is critically dependent on high-speed and high-security quantum random number generation (QRNG). In this work, we present a responsive approach to enhance the efficiency and security of QRNG by leveraging polarization-controlled heterodyne detection to simultaneously measure the quadrature amplitude and phase fluctuations of vacuum shot noise. To address the practical non-idealities inherent in QRNG systems, we investigate the critical impacts of imbalanced heterodyne detection, amplitude-phase overlap, finite-size effects, and security parameters on quantum conditional min-entropy derived from the entropy uncertainty principle. It effectively mitigates the overestimation of randomness and fortifies the system against potential eavesdropping attacks. For a high-security parameter of 10-20, QRNG achieves a true random bit extraction ratio of 83.16% with a corresponding real-time speed of 37.25 Gbps following a 16-bit analog-to-digital converter quantization and 1.4 GHz bandwidth extraction. Furthermore, we develop a deep convolutional neural network for rapid and accurate entropy evaluation. The entropy evaluation of 13,473 sets of quadrature data is processed in 68.89 s with a mean absolute percentage error of 0.004, achieving an acceleration of two orders of magnitude in evaluation speed. Extracting the shot noise with full detection bandwidth, the generation rate of QRNG using dual-quadrature heterodyne detection exceeds 85 Gbps. The research contributes to advancing the practical deployment of QRNG and expediting rapid entropy assessment.