We present an efficient method to extract the amount of true randomness that can be obtained by a quantum random number generator (QRNG). By repeating the measurements of a quantum system and by swapping between two mutually unbiased bases, a lower bound of the achievable true randomness can be evaluated. The bound is obtained thanks to the uncertainty principle of complementary measurements applied to min-entropy and max-entropy. We tested our method with two different QRNGs by using a train of qubits or ququart and demonstrated the scalability toward practical applications.
We present an efficient method to extract the amount of true randomness that can be obtained by a quantum random number generator (QRNG). By repeating the measurements of a quantum system and by swapping between two mutually unbiased bases, a lower bound of the achievable true randomness can be evaluated. The bound is obtained thanks to the uncertainty principle of complementary measurements applied to min-entropy and max-entropy. We tested our method with two different QRNGs by using a train of qubits or ququart and demonstrated the scalability toward practical applications.
Random numbers are valuable for applications ranging from cryptographic tasks to numerical simulations. Genuine randomness is generally considered possible only with a quantum system described by quantum mechanics. The dimension witness allows us to distinguish between classical and quantum scenarios, and assess the system dimensions from experimental data. Accordingly, a quantum random number generator (QRNG) based on dimension witnesses has attracted intensive study. Here we extend the prepare-and-measure QRNG protocol proposed by Brunner et al. [ Phys. Rev. Lett. 112 , 140407 ( 2014 ). PRLTAO 0031-9007 10.1103/PhysRevLett.112.140407 ] to a more general and better one. In our protocol, all the mutually unbiased bases of two-dimensional Hilbert space can be used to bound the min-entropy, which leads to a higher random number generation rate in different optical path losses and different environmental disturbances. We also demonstrate a proof-of-principle realization of our protocol, in which the random number rate increases by more photon polarization mutually unbiased bases compared with the previous one. Our method may also be applicable in higher-dimensional quantum systems.
Quantum random-number generators (QRNGs) can offer a means to generate information-theoretically provable random numbers, in principle. In practice, unfortunately, the quantum randomness is inevitably mixed with classical randomness due to classical noises. To distill this quantum randomness, one needs to quantify the randomness of the source and apply a randomness extractor. Here, we propose a generic framework for evaluating quantum randomness of real-life QRNGs by min-entropy, and apply it to two different existing quantum random-number systems in the literature. Moreover, we provide a guideline of QRNG data postprocessing for which we implement two information-theoretically provable randomness extractors: Toeplitz-hashing extractor and Trevisan's extractor.
The goal of randomness extraction is to distill (almost) perfect randomness from a weak source of randomness. When the source yields a classical string X, many extractor constructions are known. Yet, when considering a physical randomness source, X is itself ultimately the result of a measurement on an underlying quantum system. When characterizing the power of a source to supply randomness, it is hence natural to ask how much classical randomness we can extract from a quantum system. To tackle this question, we here take on the study of quantum-to-classical randomness extractors (QC-extractors). We provide constructions of QC-extractors based on measurements in a full set of mutually unbiased bases (MUBs), and certain single qubit measurements. The latter are particularly appealing since they are not only easy to implement, but also appear throughout quantum cryptography. We proceed to prove an upper bound on the maximum amount of randomness that we could hope to extract from any quantum state. Some of our QC-extractors almost match this bound. We show two applications of our results. First, we show that any QC-extractor gives rise to entropic uncertainty relations with respect to quantum side information. Such relations were previously only known for two measurements. In particular, we obtain strong relations in terms of the von Neumann (Shannon) entropy as well as the min-entropy for measurements in (almost) unitary two-designs, a full set of MUBs, and single qubit measurements in three MUBs each. Second, we resolve the central open question in the noisy-storage model by linking security to the quantum capacity of the adversary's storage device. More precisely, we show that any two party cryptographic primitives can be implemented securely as long as the adversary's storage device has sufficiently low quantum capacity. Our protocol does not need any quantum storage to implement, and is technologically feasible using present-day technology.
A quantum random number generator (QRNG) provides a reliable means for the generation of true random numbers. The inherent randomness of the vacuum fluctuations makes the quantum vacuum state a superior source of entropy. However, in practice, the raw sequences of QRNG are inevitably contaminated by classical technical noise, which compromises the security of the QRNG. Min-entropy conditioned on the classical noise is a useful method that can quantify the side-information independent randomness. To improve the extractable randomness from the raw sequences arising from the quantum vacuum-based QRNG, we propose and experimentally demonstrate two approaches, discarding-boundary-bin measurement and multi-interval sampling. The first one increases the conditional min-entropy at a low quantum-to-classical-noise ratio. The latter exploits parallel sampling using multiple analog-to-digital converters (ADCs) and effectively overcomes the finite resolution limit and uniform sampling of a single ADC. The maximum average conditional min-entropy can reach 9.2 per sample when combining these two approaches together in contrast to 6.93 with a single 8-bit ADC.
Quantum random numbers have an incomparable advantage over pseudo-random numbers since randomness originates from intrinsic property of quantum mechanics. The generation rate and the security of quantum random numbers are two significant indicators of a quantum random number generator (QRNG) for practical applications. Here we propose a mutually testing source-device-independent QRNG by simultaneously measuring a pair of conjugate quadratures from two separate parts of an untrusted continuous-variable quantum state. The amounts of randomness of the quadratures can be mutually estimated by each other via entropic uncertainty principle. Instead of randomly toggling between the conjugate quadratures of one state for collecting different types of data, two quadratures can generate check data and raw bits simultaneously and continuously in this mutually testing manner, which enhances the equivalent generation rate of private random bits to around 6 Gbit/s with a 7.5 mW laser beam. Moreover, the overall security is also improved by adjusting the conditional min-entropy in real time according to the continually monitored fluctuations of the local oscillator and the randomly measured electronic noise of homodyne detectors.
ABSTRACT Quantum random number generator (QRNG) platforms use principles of quantum mechanics to create truly random numbers. Traditional pseudo-random number generators (PRNGs) generate numbers based on deterministic formulas. QRNG's use of the principles of superposition and measurement can provide numbers that cannot be predicted or replicated; therefore, they have been used as a source of randomness in various fields. In this research project, an experimental QRNG was designed and built using Qiskit simulations. Each experiment consisted of a series of two-qubit circuits. The circuits were created to place both qubits into an equal probability state. This was done by applying a pair of Hadamard gates (Hadamard gate applies a rotation operator of π/2 radians). Then each circuit was measured. For each measurement, there would be one output from each qubit. Since the Hadamard gate creates an equal-probability superposition, the combination of each qubit will either add up to 1 or subtract from -1. These combinations will be recorded and processed through several methods to evaluate their quality. Those methods include: Shannon Entropy Analysis, Frequency Distribution Analysis and Chi-Square Uniformity Testing. Keywords: Quantum Random Number Generator, Quantum Computing, Quantum Measurement, Cryptography, Secure Randomness, Qiskit Simulation