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arXiv:2208.14986 · Applied Optics

Testing randomness of series generated in an optical Bell’s experiment

Myriam Nonaka, Mónica Agüero, Marcelo Gregorio Kovalsky, Alejandro Andrés Hnilo

Published Mar 23, 2023• 3 citations
arXivHTMLPDF

Abstract

The generation of series of random numbers is an important and difficult problem. Appropriate measurements on entangled states have been proposed as the definitive solution to produce series of certified randomness, and quantum optical systems play a major role. However, several reports indicate that random number generators based on quantum measurements have a high rate of series rejected by standard tests of randomness. This is believed to be caused by experimental imperfections and is usually solved by using classical algorithms to extract randomness. This is acceptable to generate random numbers in a single place. In quantum key distribution (QKD) instead, if the extractor is known by an eavesdropper (a situation that cannot be ruled out), the key's security may be menaced. We use a not-loophole-free, "toy" all-fiber-optic-based setup, mimicking a QKD one operating in the field, to generate binary series and evaluate their level of randomness according to Ville's principle. The series are tested with a battery of indicators of statistical and algorithmic randomness and nonlinear analysis. The good performance of a simple method to get random series from rejected ones, previously reported by Solis et al. is confirmed and supported with additional arguments. Incidentally, a theoretically predicted relationship between complexity and entropy is verified. Regarding QKD, the level of randomness of series, obtained by applying Toeplitz's extractor to rejected series, is found to be indistinguishable from the level of non-rejected raw ones.

DOI
10.1364/ao.477218

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Abstract Quantum random number generators give the opportunity to, in theory, obtain completely unpredictable numbers only perturbed by the noise in the measurement. The obtained data can be digitalized and processed so that it gives as a result a uniform sequence of binary random numbers without any relation with the classical noise in the system. In this work we analyze the performance of optical QRNGs with three different arrangements: a homodyne detector measuring vacuum fluctuations, a homodyne detector measuring amplified spontaneous emission from an EDFA and a spontaneous emission phase noise-based generator. The raw data from the experiments is processed using a Toeplitz extractor, giving as a result sequences of binary numbers capable of passing the NIST Statistical Test Suite.
Randomness is widely used in various fields, including encryption, statistical analysis, and numerical simulations. Randomness is also a fundamental resource in science and engineering. For such applications, we usually need to provide unbiased and independent random bits. This raises the issue of where to get these supposed random bits. Quantum random number generators (QRNGs) generate real random numbers based on the inherent randomness of quantum measurements. In practice, unfortunately, quantum randomness is inevitably mixed with classical randomness due to classical noise. Also, randomness is often correlated and biased. It is necessary to process the resulting raw bits sequence and convert them to good-quality output values that are as close to uniform distribution as possible. Random extractors are required for this. We analyze the randomness obtained by quantum random number generators as well as various examples of post-processing. We discuss the types of randomness extractors. Also, we use information-theoretically secure extractors and present improved novel randomness extraction.