Quantum Randomness

Minghan Li, Xingjian Zhang, Wen‐Zhao Liu +12 more

Randomness expansion where one generates a longer sequence of random numbers from a short one is viable in quantum mechanics but not allowed classically. Device-independent quantum randomness expansion provides a randomness resource of the highest security level. Here, we report the first experimental realization of device-independent quantum randomness expansion secure against quantum side information established through quantum probability estimation. We generate $5.47\ifmmode\times\else\texttimes\fi{}{10}^{8}$ quantum-proof random bits while consuming $4.39\ifmmode\times\else\texttimes\fi{}{10}^{8}\text{ }\text{ }\mathrm{bits}$ of entropy, expanding our store of randomness by $1.08\ifmmode\times\else\texttimes\fi{}{10}^{8}\text{ }\text{ }\mathrm{bits}$ at a latency of about 13.1 h, with a total soundness error $4.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$. Device-independent quantum randomness expansion not only enriches our understanding of randomness but also sets a solid base to bring quantum-certifiable random bits into realistic applications.

Art Hobson

Toyohiro Tsurumaru, Tsubasa Ichikawa, Y. Takubo +3 more

We present a no-go theorem for the distinguishability between quantum random numbers (i.e., random numbers generated quantum mechanically) and pseudorandom numbers (i.e., random numbers generated algorithmically). The theorem states that one cannot distinguish these two types of random numbers if the quantum random numbers are efficiently classically simulatable and the randomness measure used for the distinction is efficiently computable. We derive this theorem using the properties of cryptographic pseudorandom number generators, which are believed to exist in the field of cryptography. Our theorem is found to be consistent with the analyses on the actual data of quantum random numbers generated by IBM Quantum and also those obtained in the Innsbruck experiment for the Bell test, where the degrees of randomness of these two set of quantum random numbers turn out to be essentially indistinguishable from those of the corresponding pseudorandom numbers. Previous observations on the algorithmic randomness of quantum random numbers are also discussed and reinterpreted in terms of our theorems and data analyses.

Xiongfeng Ma, Feihu Xu, He Xu +3 more

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.