Abstract This work presents two significant contributions from the perspectives of quantum random number generator (QRNG) manufacturers and users. For manufacturers, the conventional method of assessing the quantumness of single-photon-based QRNGs through mean and variance comparisons of photon counts is statistically unreliable due to finite sample sizes. Given the sub-Poissonian statistics of single photons, confirming the underlying distribution is crucial for validating a QRNG’s quantumness. We propose a more efficient two-fold statistical approach to ensure the quantumness of optical sources with the desired confidence level. Additionally, we demonstrate that the output of QRNGs from exponential and uniform distributions exhibits similarity under device noise, deriving corresponding photon statistics and conditions for ε-randomness. From the user’s perspective, the fundamental parameters of a QRNG are quantumness, efficiency (entropy and random number generation rate), and cost. Our analysis reveals that these parameters depend on three factors, namely, expected photon count per unit time, external reference cycle duration, and detection efficiency. A lower expected photon count enhances entropy but increases cost and decreases the generation rate. A shorter external reference cycle boosts entropy but must exceed a minimum threshold to minimize timing errors, with minor impacts on cost and rate. Lower detection efficiency enhances entropy and lowers cost but reduces the generation rate. Finally, to validate our results, we perform statistical tests like NIST, Dieharder, AIS-31, ENT etc over the data simulated with different values of the above parameters. Our findings can empower manufacturers to customize QRNGs to meet user needs effectively.
Abstract This work presents two significant contributions from the perspectives of quantum random number generator (QRNG) manufacturers and users. For manufacturers, the conventional method of assessing the quantumness of single-photon-based QRNGs through mean and variance comparisons of photon counts is statistically unreliable due to finite sample sizes. Given the sub-Poissonian statistics of single photons, confirming the underlying distribution is crucial for validating a QRNG’s quantumness. We propose a more efficient two-fold statistical approach to ensure the quantumness of optical sources with the desired confidence level. Additionally, we demonstrate that the output of QRNGs from exponential and uniform distributions exhibits similarity under device noise, deriving corresponding photon statistics and conditions for ε-randomness. From the user’s perspective, the fundamental parameters of a QRNG are quantumness, efficiency (entropy and random number generation rate), and cost. Our analysis reveals that these parameters depend on three factors, namely, expected photon count per unit time, external reference cycle duration, and detection efficiency. A lower expected photon count enhances entropy but increases cost and decreases the generation rate. A shorter external reference cycle boosts entropy but must exceed a minimum threshold to minimize timing errors, with minor impacts on cost and rate. Lower detection efficiency enhances entropy and lowers cost but reduces the generation rate. Finally, to validate our results, we perform statistical tests like NIST, Dieharder, AIS-31, ENT etc over the data simulated with different values of the above parameters. Our findings can empower manufacturers to customize QRNGs to meet user needs effectively.
Random Number Generators (RNGs) are used in various applications, including cryptography, scientific simulations, gaming, and virtual reality. The quality of these random numbers is crucial, especially for computational approaches that rely on unpredictability to produce accurate results. In this thesis, we perform a comprehensive assessment of the quality of a novel Quantum Random Number Generator (QRNG) based on single photon. QRNGs leverage quantum mechanical properties to produce truly random numbers. This ensures high entropy, unpredictability, and security, making QRNGs particularly useful in fields that require high-quality randomness.We evaluate the statistical properties of strings generated by our QRNG and then its practical application by comparing it to traditional Pseudo-Random Number Generators (PRNGs) in Monte Carlo Integration (MCI), a technique that estimates integrals using random sampling. In particular, we use two statistical randomness test suits, namely NIST and Dieharder, to assess the statistical properties of our QRNG. All tests within these tests were passed, confirming that the corresponding QRNG achieves true randomness with sufficient high entropy. Next, we use our QRNG-generated numbers to seed Monte Carlo Integration (MCI) and compare it against results obtained using classical PRNG. The QRNG-based MCI demonstrated more accurate and stable numerical estimates, showing lower error rates and improved convergence compared to PRNG-based simulations.These findings highlight the advantages of QRNGs in enhancing numerical accuracy and computational security. While QRNGs may have slower generation rates than PRNGs, their superior randomness quality allows for more reliable Monte Carlo-based simulations, suggesting that fewer samples may be needed to achieve the same level of accuracy compared to classical PRNGs. This research underscores the potential of QRNG-powered numerical methods, paving the way for their integration into more advanced applications, including scientific computing, financial modeling, and cryptographic security.
We report a demonstration of a high-entropy optical quantum random number generator (QRNG) based on photon arrival time. We have implemented the scheme with high-speed and high-precision electronics with a time resolution of 1 ps generating 115 Mbps raw data. The random bit generation efficiency is 8 bits per detection. The experimental data is quite consistent with theoretical estimation showing minimum bias. We apply a real-time information-theoretic randomness extractor to generate a final data rate of 109 Mbps. The randomness is rigorously evaluated against well-known statistical test suites of NIST, ENT, Diehard, TU-01 and Dieharder.
Quantum random number generators (QRNGs) are an integral part of quantum key distribution (QKD) systems. To better understand the inherent physical processes, we compare the random numbers generated by two separate schemes, one is based on entropy (arrival time of photons) and another with an additional source of entropy (space) i.e, path superposition of arrival time of photons from a weak coherent source on a gated InGaAs single photon detector. Both experiments yield bits that appear random. However, they satisfy different criteria of randomness. The weak coherent source has a Poissonian distribution and extracting the variation about the arrival time of photons on gated SPD yields a source of random numbers that pass most of the Dieharder Tests. With the inclusion of superposition, we obtain random numbers that pass all the Dieharder tests. The physical origins of the random numbers in the two experiments is different, one is single entropy source based and other one is two entropy source based, and this is reflected in the outcomes of the different tests for randomness.
Quantum random number generators (QRNGs) play a crucial role in cryptography, secure communications, and stochastic simulations. This study presents the metrological characterization of a QRNG implemented on the Quandela photonic quantum computer, available via the cloud. The system generates random sequences using single photons and beam splitters, where quantum superposition ensures a fundamentally probabilistic outcome. A key aspect of this characterization involves defining the sample size and the number of qubits used. The Quandela quantum processor operates with up to six qubits, corresponding to six photons in twelve optical modes. However, the simultaneous use of multiple photons can introduce unintended correlations due to quantum interference, affecting the quality of randomness. To ensure independent bit generation, experiments were conducted with a single photon per measurement, producing one-bit outcomes per detection event. The analysis focuses on repeatability and reproducibility, examining the statistical properties of the generated sequences. Raw sequences underwent randomness testing using NIST SP800-22 and entropy assessment with NIST SP800-90B. Initial results indicate that raw sequences exhibit biases due to imperfections in single-photon sources and optical elements. The sequences generated by the Quandela photonic quantum processor failed most NIST SP800-22 tests, including Frequency (Global and Block), Runs, and Approximate Entropy, with six tests showing a 100% failure rate. Additionally, under the NIST SP800-90B evaluation, 100% of the raw sequences failed the independence and identically distributed (IID) test, highlighting strong correlations and statistical dependencies. To enhance randomness quality, post-processing techniques were applied, including Von Neumann and the combination Samuelson + Von Neumann extractors. These methods significantly improved bit balance and reduced statistical dependencies. After post-processing, all sequences passed the NIST SP800-90B IID test, and the entropy per bit increased to 0.771 ± 0.005 for the Ascella processor, ensuring improved randomness quality. The findings highlight the metrological challenges in QRNGs based on photonic quantum processors, emphasizing the need for rigorous statistical validation. Despite system-specific noise, the quantum origin of randomness remains preserved, ensuring that the extracted sequences retain their fundamental unpredictability. Additionally, limitations associated with photonic quantum systems, such as hardware imperfections, photon losses, and optical misalignment, are discussed in the context of their impact on randomness quality. Despite these limitations, rigorous statistical validation and post-processing enable the generation of high-quality random sequences suitable for cryptographic protocols, secure key distribution, and high-performance computing This study reinforces the importance of metrology in quantum technologies, providing a structured methodology for optimizing QRNG reliability and performance.
Quantum random number generators (QRNG) are the prime source of randomness, by exploiting the unpredictable nature of Quantum mechanics QRNG aims to provide a string of completely random utterly unpredictable numbers. QRNGs are crucial for cryptography, scientific calculation, simulation, and many more real-world applications. Our Optical Quantum Random Number Generator (OQRNG) utilizes a high-speed pulsating laser, a Polarizing beam splitter (PBS), photodetectors, and advanced signal processing units that capture and digitize random photon intensity forming the raw random bit stream. This technique is famously known as Branching Path Technique. After that, we implement rigorous testing that encompasses the statistical randomness tests developed by National Institute of Standards and Technology (NIST) to ensure the guaranteed ran-domness meets security standards. A user-friendly Graphic user interface (GUI) simplifies interaction with the QRNG allowing the user to configure device settings, monitor system performance, and securely extract random numbers. Our findings help us demonstrate the superiority of QRNGs over classical random number generators, and highlight the potential of photon-based QRNGs and their environmentally friendly and efficient random number generation.