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arXiv:2401.08325 · Optics Express

Quantum random number generation based on phase reconstruction

Jialiang Li, Zitao Huang, Chunlin Yu, Jiajie Wu, Tongge Zhao, Xiangwei Zhu, Shi‐Hai Sun

Published Jan 18, 2024• 9 citations
arXivHTMLPDF

Abstract

Quantum random number generator (QRNG) utilizes the intrinsic randomness of quantum systems to generate completely unpredictable and genuine random numbers, finding wide applications across many fields. QRNGs relying on the phase noise of a laser have attracted considerable attention due to their straightforward system architecture and high random number generation rates. However, traditional phase noise QRNGs suffer from a 50% loss of quantum entropy during the randomness extraction process. In this paper, we propose a phase-reconstruction quantum random number generation scheme, in which the phase noise of a laser is reconstructed by simultaneously measuring the orthogonal quadratures of the light field using balanced detectors. This enables direct discretization of uniform phase noise, and the min-entropy can achieve a value of 1. Furthermore, our approach exhibits inherent robustness against the classical phase fluctuations of the unbalanced interferometer, eliminating the need for active compensation. Finally, we conducted experimental validation using commercial optical hybrid and balanced detectors, achieving a random number generation rate of 1.96 Gbps at a sampling rate of 200 MSa/s.

DOI
10.1364/oe.515390

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Quantum random number generator (QRNG) utilizes the intrinsic randomness of quantum systems to generate completely unpredictable and genuine random numbers, finding wide applications across many fields. QRNGs relying on the phase noise of a laser have attracted considerable attention due to their straightforward system architecture and high random number generation rates. However, traditional phase noise QRNGs suffer from a 50% loss of quantum entropy during the randomness extraction process. In this paper, we propose a phase-reconstruction quantum random number generation scheme, in which the phase noise of a laser is reconstructed by simultaneously measuring the orthogonal quadratures of the light field using balanced detectors. This enables direct discretization of uniform phase noise, and the min-entropy can achieve a value of 1. Furthermore, our approach exhibits inherent robustness against the classical phase fluctuations of the unbalanced interferometer, eliminating the need for active compensation. Finally, we conducted experimental validation using commercial optical hybrid and balanced detectors, achieving a random number generation rate of 1.96 Gbps at a sampling rate of 200 MSa/s.
The speed of a quantum random number generator is essential for practical applications, such as high-speed quantum key distribution systems. Here, we push the speed of a quantum random number generator to 68 Gbps by operating a laser around its threshold level. To achieve the rate, not only high-speed photodetector and high sampling rate are needed but also a very stable interferometer is required. A practical interferometer with active feedback instead of common temperature control is developed to meet the requirement of stability. Phase fluctuations of the laser are measured by the interferometer with a photodetector and then digitalized to raw random numbers with a rate of 80 Gbps. The min-entropy of the raw data is evaluated by modeling the system and is used to quantify the quantum randomness of the raw data. The bias of the raw data caused by other signals, such as classical and detection noises, can be removed by Toeplitz-matrix hashing randomness extraction. The final random numbers can pass through the standard randomness tests. Our demonstration shows that high-speed quantum random number generators are ready for practical usage.
In 2010 Qi et al. [Opt. Lett.35(3), 312 (2010)] demonstrated a random number generator based on the drift of the phase of a laser due to spontaneous emission, The out-of-the-lab implementation of this scheme presents two main drawbacks: it requires a long and highly unbalanced interferometer to generate a random phase with uniform probability distribution, or alternatively, a shorter and slightly unbalanced interferometer that notwithstanding requires active stabilization and does not generate a uniform probability distribution without randomness extraction. Here we demonstrate that making use of the random nature of the phase difference between two independent laser sources and two coherent detectors we can overcome these limitations. The two main advantages of the system demonstrated are: i) it generates a probability distribution of quantum origin which is intrinsically uniform and thus in principle needs no randomness extraction for obtaining a uniform distribution, and ii) the phase is measured with telecom equipment routinely used for high capacity coherent optical communications. The speed of random bit generation is determined by the photodetector bandwidth and the linewidth of the lasers. As a by-product of our method, we have obtained images of how phase noise develops with time in a laser. This provides a highly visual alternative way of measuring the coherence time of a laser.
Abstract As a fundamental phenomenon in nature, randomness has a wide range of applications in the fields of science and engineering. Among different types of random number generators (RNG), quantum random number generator (QRNG) is a kind of promising RNG as it can provide provable true random numbers based on the inherent randomness of fundamental quantum processes. Nevertheless, the randomness from a QRNG can be diminished (or even destroyed) if the devices (especially the entropy source devices) are not perfect or ill-characterized. To eliminate the practical security loopholes from the source, source-independent QRNGs, which allow the source to have arbitrary and unknown dimensions, have been introduced and become one of the most important semi-device-independent (DI) QRNGs. Herein a method that enables ultra-fast unpredictable quantum random number generation from quadrature fluctuations of quantum optical field without any assumptions on the input states is proposed. Particularly, to estimate a lower bound on the extractable randomness that is independent from side information held by an eavesdropper, a new security analysis framework is established based on the extremality of Gaussian states, which can be easily extended to design and analyze new semi-DI continuous variable QRNG protocols. Moreover, the practical imperfections of the QRNG including the effects of excess noise, finite sampling range, finite resolution and asymmetric conjugate quadratures are taken into account and quantitatively analyzed. Finally, the proposed method is experimentally demonstrated to obtain high secure random number generation rates of 15.07 Gbits s −1 in off-line configuration and can potentially achieve 6 Gbits s −1 by real-time post-processing.
Aiming at the problem that the current Quantum Random Number Generator (QRNG) cannot simultaneously meet the high-speed and real-time requirements of random number generation in quantum key distribution communication, this paper improves the QRNG scheme based on pulse laser as light source to extract phase information. The random phase information is converted into light intensity information by single-mode Michelson interferometer, and then converted into electrical signal by high-speed Photo Detector (PD). Finally, the real-time quantum random number generation rate of 1.1 Gbit/s is obtained by using 16 bit Analog-to-Digital Converter (ADC) with 250 MHz sampling rate and 50% extraction rate. A high-speed, real-time and integrated QRNG equipment is realized. At the same time, the advantages of this scheme and continuous laser as light source in principle and system design are compared. QRNG based on pulsed laser light source has passed various tests of China Academy of Information and Communications. The random number output by the product in the process of stable operation can pass 15 test standards specified in the State Cryptography Administration randomness test document GB/T 32915-2016 and National Institute of Standards and Technology (NIST) test standards.
Quantum random number generators are essential for achieving information-theoretical security in modern cryptographic systems. Among various implementations, laser phase noise schemes are widely favored for their simple architecture and high integration potential. However, the intrinsic correlations in the raw data are often neglected, which violates the independent and identically distributed assumption and potentially compromises system security. In this work, we establish an analytical model of correlation and formulate an analytical expression for the conditional min-entropy in the presence of intrinsic correlations to accurately quantify the genuinely extractable randomness. The validity of our theoretical model is confirmed by numerical simulations and experimental results, exhibiting excellent agreement. Under typical setups it is shown that neglecting intrinsic correlations leads to an overestimation of extractable randomness by approximately 46%. This work provides a valuable theoretical framework for designing compact, high-performance quantum random number generators with rigorous security analysis.
The quantum random number generator (QRNG) operates based on fundamental quantum mechanical principles to produce high-quality random numbers. Recently, chip-based QRNGs have garnered significant attention due to their compact size, low cost, and reduced power consumption. In this work, we demonstrate a hybrid integrated QRNG leveraging continuous-wave (CW) laser phase fluctuations. Using advanced hybrid packaging techniques, we integrate a tunable, unbalanced Mach-Zehnder interferometer (uMZI), laser, and InGaAs photodiode (PD) within a 14-pin butterfly package. To enhance the long-term stability and reliability of the QRNG, a negative temperature coefficient (NTC) thermistor is also attached to the chip for thermal regulation. The resulting integrated QRNG has a footprint of just 30 mm × 12.7 mm, and delivers a random number generation rate of 4.68 Gbps after min-entropy evaluation and post-processing. The combination of compact size and high-speed performance makes this hybrid integrated QRNG ideal for high-speed, large-scale applications.