Quantum random number generators offer various ways of generating entropy based on inherently nondeterministic physical processes, thus guaranteeing the quality and security of their output. While the expected output of random number generators is a uniformly distributed stream of bits, actual physical measurement statistics typically follow some other distribution, mandating additional post-processing steps. We present a post-processing scheme inspired by the continuous probability integral transform that can be used with the typically discrete distributions of physical measurement statistics to produce a close to uniformly distributed output bitstream. We give bounds on the maximum bias of the output and also show a way to produce output that is arbitrarily close statistically to the expected uniform distribution in an ideal scenario. While the scheme can be used with any input distribution, we utilized a photonic time-of-arrival based architecture to give a practical example of usage and acquire experimental results, which we statistically tested with the NIST Statistical Test Suite.
Quantum random number generators offer various ways of generating entropy based on inherently nondeterministic physical processes, thus guaranteeing the quality and security of their output. While the expected output of random number generators is a uniformly distributed stream of bits, actual physical measurement statistics typically follow some other distribution, mandating additional post-processing steps. We present a post-processing scheme inspired by the continuous probability integral transform that can be used with the typically discrete distributions of physical measurement statistics to produce a close to uniformly distributed output bitstream. We give bounds on the maximum bias of the output and also show a way to produce output that is arbitrarily close statistically to the expected uniform distribution in an ideal scenario. While the scheme can be used with any input distribution, we utilized a photonic time-of-arrival based architecture to give a practical example of usage and acquire experimental results, which we statistically tested with the NIST Statistical Test Suite.
Utilizing the inherently unpredictable nature of quantum mechanics, quantum random number generators (QRNGs) can provide randomness for applications where quality entropy (like in the case of cryptography) is essential. We present a post-processing scheme utilizing min-entropy estimation and hashing for optical QRNGs based on measuring individual photon arrival times. Our method allows for the handling of possible errors due to non-ideal components or even a potential attacker, given some basic assumptions to reliably produce a safe, good quality, uniformly distributed bitstream as output. We validate our results with an intentionally non-ideal measurement setup to show robustness, while also statistically testing our final output with four popular statistical test suites.
Quantum random number generators can deliver entropy based on inherently non-deterministic physical phenomena, which is essential for applications where quality randomness is needed (e.g. in cryptography). Our generator based on photon time-of-arrival exploits the randomness of light emission in semiconductors. To measure the time between detections we use a continuous (non-restartable) clock for time tagging, which permits simpler hardware but produces slightly different output from the optimal exponential distribution. To handle this and produce quality output, we use Toeplitz hashing based bit generation after modeling and calculating a lower bound of extractable min-entropy for the general case of this generation scheme with a continuous clock. We produced uniformly distributed output bits with our setup, while also reaching a generation efficiency of 9.75 output bits per 16-bit input record, which is an improvement to our previously used method. Our generator has also been statistically tested using four of the popular statistical test suites.
We present an integrated photonic quantum random number generator combining photon-path selection and time-delay encoding methods to efficiently produce high-quality random bits. True random number generators, particularly quantum-based random number generators, play a critical role in secure communications, cryptographic protocols, and simulations, as they provide genuine unpredictability derived from fundamental quantum processes. This study presents the development of an optical random number generator utilizing a photonic chip, resulting in a very stable, compact, and high key-to-signal ratio device. Our setup employs an attenuated pulsed laser source combined with a photonic circuit featuring a multi-mode interference, whose outputs are monitored by single-photon avalanche diodes. For photon-path encoding, a von Neumann extractor effectively reduces output bias by discarding correlated detection events. In addition, we measure photon arrival times (time-delay encoding) using a novel bin-merging and modulo-based encoding strategy to counteract hardware-induced biases, achieving near-ideal bit uniformity. Experimental results show that combining both encoding techniques doubles the bit-generation rate compared to path-encoding only, achieving 0.49 bits per signal while simultaneously meeting stringent randomness criteria validated by passing all tests in the NIST statistical test suite.
We demonstrate a viable source of unbiased quantum random numbers whose statistical properties can be arbitrarily programmed without the need for any postprocessing such as randomness distillation or distribution transformation. It is based on measuring the arrival time of single photons in shaped temporal modes that are tailored with an electro-optical modulator. We show that quantum random numbers can be created directly in customized probability distributions and pass all randomness tests of the NIST and Dieharder test suites without any randomness extraction. The min-entropies of such generated random numbers are measured close to the theoretical limits, indicating their near-ideal statistics and ultrahigh purity. Easy to implement and arbitrarily programmable, this technique can find versatile uses in a multitude of data analysis areas.
We demonstrate a novel high speed and multi-bit optical quantum random number generator by continuously measuring arrival time of photons with a common starting point. To obtain the unbiased and post-processing free random bits, the measured photon arrival time is converted into the sum of integral multiple of a fixed period and a phase time. Theoretical and experimental results show that the phase time is an independent and uniform random variable. A random bit extraction method by encoding the phase time is proposed. An experimental setup has been built and the unbiased random bit generation rate could reach 128 Mb/s, with random bit generation efficiency of 8 bits per detected photon. The random numbers passed all tests in the statistical test suite.
Random numbers are fundamental elements in different fields of science and technology such as computer simulation like Monte Carlo-method simulation, statistical sampling, cryptography, games and gambling, and other areas where unpredictable results are necessary. Random number generators (RNG) are generally classified as “pseudo”-random number generators (PRNG) and "truly" random number generators (TRNG). Pseudo random numbers are generated by computer algorithms with a (random) seed and a specific formula. The random numbers produced in this way (with a small degree of unpredictability) are good enough for some applications such as computer simulation. However, for some other applications like cryptography they are not completely reliable. When the seed is revealed, the entire sequence of numbers can be produced. The periodicity is also an undesirable property of PRNGs that can be disregarded for most practical purposes if the sequence recurs after a very long period. However, the predictability still remains a tremendous disadvantage of this type of generators. Truly random numbers, on the other hand, can be generated through physical sources of randomness like flipping a coin. However, the approaches exploiting classical motion and classical physics to generate random numbers possess a deterministic nature that is transferred to the generated random numbers. The best solution is to benefit from the assets of indeterminacy and randomness in quantum physics. Based on the quantum theory, the properties of a particle cannot be determined with arbitrary precision until a measurement is carried out. The result of a measurement, therefore, remains unpredictable and random. Optical phenomena including photons as the quanta of light have various random, non-deterministic properties. These properties include the polarization of the photons, the exact number of photons impinging a detector and the photon arrival times. Such intrinsically random properties can be exploited to generate truly random numbers. Silicon (Si) is considered as an interesting material in integrated optics. Microelectronic chips made from Si are cheap and easy to mass-fabricate, and can be densely integrated. Si integrated optical chips, that can generate, modulate, process and detect light signals, exploit the benefits of Si while also being fully compatible with electronic. Since many electronic components can be integrated into a single chip, Si is an ideal candidate for the production of small, powerful devices. By complementary metal-oxide-semiconductor (CMOS) technology, the fabrication of compact and mass manufacturable devices with integrated components on the Si platform is achievable. In this thesis we aim to model, study and fabricate a compact photonic quantum random number generator (QRNG) on the Si platform that is able to generate high quality, "truly" random numbers. The proposed QRNG is based on a Si light source (LED) coupled with a Si single photon avalanche diode (SPAD) or an array of SPADs which is called Si photomultiplier (SiPM). Various implementations of QRNG have been developed reaching an ultimate geometry where both the source and the SPAD are integrated on the same chip and fabricated by the same process. This activity was performed within the project SiQuro—on Si chip quantum optics for quantum computing and secure communications—which aims to bring the quantum world into integrated photonics. By using the same successful paradigm of microelectronics—the study and design of very small electronic devices typically made from semiconductor materials—, the vision is to have low cost and mass manufacturable integrated quantum photonic circuits for a variety of different applications in quantum computing, measure, sensing, secure communications and services. The Si platform permits, in a natural way, the integration of quantum photonics with electronics. Two methodologies are presented to generate random numbers: one is based on photon counting measurements and another one is based on photon arrival time measurements. The latter is robust, masks all the drawbacks of afterpulsing, dead time and jitter of the Si SPAD and is effectively insensitive to ageing of the LED and to its emission drifts related to temperature variations. The raw data pass all the statistical tests in national institute of standards and technology (NIST) tests suite and TestU01 Alphabit battery without a post processing algorithm. The maximum demonstrated bit rate is 1.68 Mbps with the efficiency of 4-bits per detected photon. In order to realize a small, portable QRNG, we have produced a compact configuration consisting of a Si nanocrystals (Si-NCs) LED and a SiPM. All the statistical test in the NIST tests suite pass for the raw data with the maximum bit rate of 0.5 Mbps. We also prepared and studied a compact chip consisting of a Si-NCs LED and an array of detectors. An integrated chip, composed of Si p+/n junction working in avalanche region and a Si SPAD, was produced as well. High quality random numbers are produced through our robust methodology at the highest speed of 100 kcps. Integration of the source of entropy and the detector on a single chip is an efficient way to produce a compact RNG. A small RNG is an essential element to guarantee the security of our everyday life. It can be readily implemented into electronic devices for data encryption. The idea of "utmost security" would no longer be limited to particular organs owning sensitive information. It would be accessible to every one in everyday life.