Abstract
Random number generation plays an essential role in technology with important applications in areas ranging from cryptography to Monte Carlo methods, and other probabilistic algorithms. All such applications require high-quality sources of random numbers, yet effective methods for assessing whether a source produce truly random sequences are still missing. Current methods either do not rely on a formal description of randomness (NIST test suite) on the one hand, or are inapplicable in principle (the characterization derived from the Algorithmic Theory of Information), on the other, for they require testing all the possible computer programs that could produce the sequence to be analysed. Here we present a rigorous method that overcomes these problems based on Bayesian model selection. We derive analytic expressions for a model’s likelihood which is then used to compute its posterior distribution. Our method proves to be more rigorous than NIST’s suite and Borel-Normality criterion and its implementation is straightforward. We applied our method to an experimental device based on the process of spontaneous parametric downconversion to confirm it behaves as a genuine quantum random number generator. As our approach relies on Bayesian inference our scheme transcends individual sequence analysis, leading to a characterization of the source itself.
Highlights
Random numbers have acquired an essential role in our daily lives because of our close relationship with communication devices and technology
A new alternative has been proposed by exploiting the inherently probabilistic nature of quantum mechanical systems. These Quantum Random Number Generators (QRNGs) are in principle superior to their classical counterparts and recent experiments have shown ref. 1 that they can reach the same quality as commercial pseudo-random number generators (pRNGs)
The suite is based on testing certain features of random sequences that are hard to reproduce algorithmically, such as its power spectrum, longest string of consecutive 1’s, and so on
Summary
Rafael Díaz Hernández Rojas[1], Aldo Solís[2], Alí M. This (un)certainty quantification is the hallmark of Bayesian statistics, since P( sym|s) represents the probability that modelling our QRNG as a random source is correct Computing this posterior distribution directly from Bayes’ Theorem, Eq 6, we arrive at the values shown in Table 1 for each β. These two criteria combined lead us to conclude that there is decisive evidence for our hypothesis that sym is the underlying model driving our source, verifying that the photonic RNG is strictly random in the sense described in the article. A simplified analysis can be performed with the BN-type bounds given in Section 3 of the SI, which leads to more stringent criteria than other approaches
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