Quantum coherence serves as a fundamental resource for generating intrinsic randomness, yet the quantification of randomness in quantum random number generators (QRNGs) based on spontaneous emission has remained largely phenomenological. Existing randomness analysis lacks rigorous adversarial models and a clear characterization of the role of quantum coherence in these systems. In this work, we develop a comprehensive quantum information-theoretic framework for randomness generation in spontaneous emission processes. We characterize two distinct eavesdropping strategies: one where the adversary directly accesses the atom ensemble, and the other where the adversary accesses only its purification. Our analysis reveals that when randomness is generated through single-photon detection and temporal mode measurements, the QRNG is vulnerable to the first adversary scenario, though it still guarantees a lower bound on intrinsic randomness against the second adversary scenario even under maximal information leakage from the atoms. In contrast, QRNGs based on spatial mode detection and phase fluctuations demonstrate security against both types of adversaries, providing robust randomness generation. Furthermore, we provide a quantitative calculation of intrinsic randomness for these spontaneous-emission-based QRNG schemes.
Journal reference
Fluctuation and Noise Letters 25(2) (2026) 2540031
Quantum coherence serves as a fundamental resource for generating intrinsic randomness, yet the quantification of randomness in quantum random number generators (QRNGs) based on spontaneous emission has remained largely phenomenological. Existing randomness analysis lacks rigorous adversarial models and a clear characterization of the role of quantum coherence in these systems. In this work, we develop a comprehensive quantum information-theoretic framework for randomness generation in spontaneous emission processes. We characterize two distinct eavesdropping strategies: one where the adversary directly accesses the atom ensemble, and the other where the adversary accesses only its purification. Our analysis reveals that when randomness is generated through single-photon detection and temporal mode measurements, the QRNG is vulnerable to the first adversary scenario, though it still guarantees a lower bound on intrinsic randomness against the second adversary scenario even under maximal information leakage from the atoms. In contrast, QRNGs based on spatial mode detection and phase fluctuations demonstrate security against both types of adversaries, providing robust randomness generation. Furthermore, we provide a quantitative calculation of intrinsic randomness for these spontaneous-emission-based QRNG schemes.
Abstract The amplified spontaneous emission (ASE) noise has been extensively studied and employed to build quantum random number generators (QRNGs). While the previous relative works mainly focus on the realization and verification of the QRNG system, the comprehensive physical model and randomness quantification for the general detection of the ASE noise are still incomplete, which is essential for the quantitative security analysis. In this paper, a systematical physical model for the detection and acquisition of the ASE noise with added electronic noise is developed and verified, based on which the numerical simulations are performed under various setups and the simulation results all significantly fit well with the corresponding experimental data. Then, a randomness quantification method and the corresponding experimentally verifiable approach are proposed and validated, which quantifies the randomness purely resulted from the quantum process and improves the security analysis for the QRNG based on the detection of the ASE noise. The physical model and the randomness quantification method proposed in this paper are of significant feasibility and applicable for the QRNG system with randomness originating from the detection of the photon number with arbitrary distributions.
Random numbers play a key role in information science, especially in cryptography. Based on the probabilistic nature of quantum mechanics, quantum random number generators can produce genuine randomness. In particular, random numbers can be produced from laser phase fluctuations with a very high speed, typically in the Gbps regime. In this work, by developing a physical model, we investigate the origin of the randomness in quantum random number generators based on laser phase fluctuations. We show how the randomness essentially stems from spontaneous emissions. The laser phase fluctuation can be quantitatively evaluated from basic principles and qualitatively explained by the Brownian motion model. After taking account of practical device precision, we show that the randomness generation speed is limited by the finite resolution of detection devices. Our result also provides the optimal experiment design in order to achieve the maximum generation speed.
Quantum random number generators (QRNGs) offer a fundamentally different approach to random number generation compared to classical methods, leveraging the inherent randomness of quantum processes. However, their practical implementation and analysis often face challenges, particularly concerning the accurate characterization of the underlying probability distribution and the optimization of generation algorithms. This paper presents a comprehensive probability analysis of QRNG output, focusing on identifying and quantifying sources of bias and uncertainty. We introduce a novel framework combining quantum information theory and statistical analysis to rigorously evaluate QRNG performance. Furthermore, we propose an optimization strategy based on adaptive sampling techniques and error correction, aiming to enhance both the security and efficiency of QRNGs. Our approach provides a detailed understanding of QRNG behavior and offers actionable insights for designing and deploying robust QRNG systems. The core of our analysis lies in the precise determination of the output probability distribution, denoted as P(s1, s2, ..., sK), where K represents the number of bits generated. We demonstrate how this distribution can be refined through iterative statistical estimation and how this information can be used to improve the generation process.
Quantum random number generators (QRNGs) harness the intrinsic randomness in measurement processes: the measurement outputs are truly random given the input state is a superposition of the eigenstates of the measurement operators. We show in the case of trusted devices, genuine randomness could be generated even when the input to the detector is a mixed state. We propose a random number generation scheme based on measuring the quadrature fluctuations of a single mode thermal state with an optical homodyne detector. By interfering a broadband incoherent source with a single mode local oscillator at a beam splitter and performing differential photodetection, we can selectively detect the quadrature fluctuations of a single mode of the incoherent source, thanks to the filtering function introduced by the local oscillator. Experimentally, a quadrature variance about three orders of magnitude larger than the vacuum noise is observed from an amplified spontaneous emission source, suggesting this scheme can tolerate much high technical noises in comparison with QRNGs based on measuring the vacuum noise. The high quality of this entropy source is evidenced by the small correlation coefficients of the acquired data.
Randomness is essential ingredient for applications in cryptography, stochastic simulation, and fundamental science experiments [American Scientist 89, 4 (2001); PRL 115, 25 (2015)]. Common practice is to generate random numbers from mathematical algorithm using Pseudo-random number generators. We are interested in tackling this problem with quantum technology. Phase diffusion in spontaneous emission events is a quantum phenomena with inherent randomness [Opt. Express 19, 21 (2011)]. Implementations of this scheme using pulsed lasers can yield high-speed quantum random number generation (QRNG) [Opt. Express 22, 2 (2014)]. The general interest in the laser phase diffusion QRNG setup has been mainly focused on and motivated by the speed of the random number generations. Little has been stated about the performance of quantum phase noise as a randomness source in QRNG, from the perspective of the physics involved. We reanalyze the process of phase diffusion based QRNG and give an intuitive explaining picture of the underlying physics. Our findings show that a pulsed process is beneficial over the continuous-wave approach and give a upper bound of maximum random bit rate for a given experimental setting. In detail, the output of a semiconductor laser contains fluctuations in intensity and phase. This was originally studied first by Charles Henry in 1982 [J. Lightwave Techn. 4, 3 (1986)]. Based on that one can identify two phenomena contributing to the phase noise, which takes the form of a random walk. First, there will be phase changes due to the carrier-induced change in refractive index in the semiconductor laser. Second, spontaneous emission events take place in the active medium [Opt. Express 19, 21 (2011)]. Naturally, taking spontaneous emission events into account necessitates the application of stochastic laser rate equations for theoretical description. We solve these equations numerically be a Monte-Carlo simulation and investigate several random walk scenarios. One of our essential findings is that the phase fluctuation becomes much larger in the pulsed laser regime than in the continuous-wave mode. Additionally, there is a natural limit on the maximum pulse repetition rate for a given pulse width, since the phase jumps become smaller for shorter pulse distances. Since phase measurement is not a feasible procedure for optical signals, the phase fluctuation needs to be converted to an observable macroscopic parameter such as the optical intensity. This can be done by using an interferometer setup. The whole experimental setting is shown in Fig. 2 (left). An DFB laser diode is modulated using gain-switching technique to generate uniform amplitude signals with random phases. Each signal interferes with neighboring pulses through an unbalanced Mach-Zehnder interferometer. The delay in one arm was set to equal to the pulse repetition rate. With this setup we investigate the influence of several parameters on the shape of the probability distribution determining the quality of QRNG. The theoretical as well as experimental findings can help to find physical standards for QRNG verification rather than the ones based on classical statistical information theory.
Quantum random number generators (QRNGs) offer a fundamentally different approach to random number generation compared to classical methods, leveraging the inherent unpredictability of quantum mechanical processes. However, the widespread adoption of QRNGs is currently hindered by a lack of standardized verification procedures and effective multi-model fusion strategies. This paper addresses these challenges by proposing a comprehensive framework for the multi-model validation and fusion of QRNGs. The framework integrates multiple quantum physical and information-theoretic randomness sources, employing statistical modeling for rigorous security assessments. Specifically, we introduce a novel approach to quantifying the entropy and bias of QRNG outputs across various models. The core contribution lies in establishing a systematic methodology for evaluating QRNG security and presenting a viable strategy for combining the strengths of different QRNG technologies. Our analysis highlights the importance of diverse validation techniques and the potential for improved QRNG performance through model fusion. The proposed framework provides a foundation for more reliable and trustworthy QRNG implementations, crucial for applications demanding high-quality randomness, such as cryptography and simulation.