Random numbers are at the heart of diverse fields, ranging from simulations of stochastic processes to classical and quantum cryptography. The requirement for true randomness in these applications has motivated various proposals for generating random numbers based on the inherent randomness of quantum systems. The generation of true random numbers with arbitrarily defined probability distributions is highly desirable for applications, but it is very challenging. Here we show that single-photon quantum walks can generate multi-bit random numbers with on-demand probability distributions, when the required "coin" parameters are found with the gradient descent (GD) algorithm. Our theoretical and experimental results exhibit high fidelity for various selected distributions. This GD-enhanced single-photon system provides a convenient way for building flexible and reliable quantum random number generators. Multi-bit random numbers are a necessary resource for high-dimensional quantum key distribution.
Random numbers are at the heart of diverse fields, ranging from simulations of stochastic processes to classical and quantum cryptography. The requirement for true randomness in these applications has motivated various proposals for generating random numbers based on the inherent randomness of quantum systems. The generation of true random numbers with arbitrarily defined probability distributions is highly desirable for applications, but it is very challenging. Here we show that single-photon quantum walks can generate multi-bit random numbers with on-demand probability distributions, when the required "coin" parameters are found with the gradient descent (GD) algorithm. Our theoretical and experimental results exhibit high fidelity for various selected distributions. This GD-enhanced single-photon system provides a convenient way for building flexible and reliable quantum random number generators. Multi-bit random numbers are a necessary resource for high-dimensional quantum key distribution.
The generation of true randomness remains a significant challenge in computer science, particularly when relying solely on classical algorithms. Many current approaches employ pseudo-random number generators (PRNGs), which, despite their computational efficiency, are inherently predictable and lack genuine randomness. This paper proposes a novel method for algorithmic randomness generation leveraging the principles of quantum walks. We demonstrate that the inherent uncertainty and superposition properties of quantum systems provide a robust mechanism for generating truly random numbers. Specifically, we outline a framework for designing quantum walks on graphs, where the evolution of the walker's state is fundamentally probabilistic and unpredictable. The core of our approach resides in exploiting the quantum walk's non-deterministic nature to produce sequences of numbers that exhibit statistical properties consistent with true randomness. The theoretical framework is presented, including a detailed description of the mathematical formalism underlying the quantum walk and the probability distribution of the walker's positions. We highlight the potential advantages of this approach, particularly in scenarios demanding high-quality randomness for cryptographic applications or simulations. The key concept is to translate a classical problem into a quantum one, where the inherent probabilistic nature of quantum mechanics offers a superior solution to the problem of generating genuine randomness.
Abstract Measurement outcomes on quantum systems exhibit inherent randomness and are fundamentally nondeterministic. This has enabled quantum physics to set new standards for the generation of true randomness with significant applications in the fields of cryptography, statistical simulations, and modeling of the nondeterministic behavior in various other fields. In this work, we present a scheme for the generation of multi-bit random numbers using path-entangled single photons. For the experimental demonstration, we generate a path-entangled state using single photons from spontaneous parametric down-conversion (SPDC) and assign a multi-qubit state for them in path basis. One-bit and two-bit random numbers are then generated by measuring entangled states in the path basis. In addition to passing the NIST tests for randomness, we also demonstrate the certification of quantumness and self-certification of quantum random number generator (QRNG) using Clauser, Horne, Shimony and Holt (CHSH) inequality violation. We also record the significantly low autocorrelation coefficient from the raw bits generated and this along with CHSH violation rules out multi-photon events and ensure the protection from photon splitting attack. Distribution of photons along multiple paths resulting in multiple bits from one photon extends the limit on bit generation rate imposed by the detection dead time of the individual detector. Thus, the path-entangled states can generate higher bitrates compared to scheme using entangled photon pair which are limited by the coincidence counts. We demonstrate this by generating a high rate of about 80 Mbps when the single photon detector saturates at around 28 Mcps and still show violation of CHSH inequality.
Random numbers are a fundamental resource in science and engineering, and are also widely used in many fields, such as simulation, cryptography, lotteries, fundamental science. There are algorithmically generated numbers that look like random numbers but are not truly random. These pseudo random numbers are generated from a computer, using deterministic algorithms. Because, we cannot use pseudo random generators in situations, where true randomness is necessary, we use true random number generators. In this case, we use unpredictable random events as a random source. Quantum random number generators (QRNG) output true random numbers based on inherent randomness in quantum measurements. Our goal is to generate fast random numbers at a lower cost. At the same time, a high level of randomness is essential. We present the improved novel quantum random number generator, which is based the on time of arrival QRNG. It is rather efficient, as it uses the simple version of the detectors with rather few requirements. The novel QRNG produces more than one random bit per each photon detection.
Abstract We present a scheme for multi-bit quantum random number generation using a single qubit discrete-time quantum walk in one-dimensional space. Irrespective of the initial state of the qubit, quantum interference and entanglement of particle with the position space in the walk dynamics certifies high randomness in the system. Quantum walk in a position space of dimension 2l + 1 ensures string of (l + 2)-bits of random numbers from a single measurement. Bit commitment with the position space and control over the spread of the probability distribution in position space enable us with options to extract multi-bit random numbers. This highlights the power of one qubit, its practical importance in generating multi-bit string in single measurement and the role it can play in quantum communication and cryptographic protocols. This can be further extended with quantum walks in higher dimensions.
This paper presents the design and theoretical framework for a quantum random number generator (QRNG) rooted in the principles of quantum mechanics. The core innovation lies in leveraging the inherent randomness associated with quantum measurement, specifically the uncertainty principle, to generate truly random numbers, a significant departure from the limitations of classical random number generators. The proposed system utilizes a measurement process involving a quantum system, such as a photon polarization or a quantum bit, to produce a sequence of random bits. The generated bits are then processed to eliminate bias and ensure high uniformity. The theoretical analysis focuses on quantifying the randomness inherent in the measurement process and demonstrating the potential for generating high-quality random numbers. This work addresses the growing demand for secure communication, cryptography, and simulation applications that require truly random numbers, offering a fundamentally different approach compared to traditional methods.
This paper proposes and demonstrates an optical quantum random number generator based on distribution of single photon pulse amplitude of a photomultiplier tube.The light emitted from ultraviolet LED is attenuated into discrete single photon sequence.After these photons are detected by the photomultiplier tube,the single-photon pulses with random distribution are output.Digital values of peaks of these single-photon pulses are used as the entropy sources of random number generation.In order to reduce the bias of the raw extracted random number,the SHA-256 post processing method based on FPGA is proposed and implemented.When our designed quantum random number generator works at a counting rate of 500kc/s,7random bits can be extracted on average per detected photon,and a random number generation rate of 3.5Mbit/s is obtained.The random bit sequences are tested by random number test programs ENT and STS.The test results show that the generated random bit sequences fully meet the standards of true random numbers.