Random numbers certified by Bell’s theorem

By Stefano Pironio, Antonio Acín, Serge Massar, A. B. D. L. Giroday, Dzmitry N. Matsukevich, Peter Maunz, S. Olmschenk, D. Hayes, L. Luo, T. Manning and 1 more. Nature, 2009

1,458 citations recorded by the source corpus.

Randomness is a fundamental feature of nature and a valuable resource for applications ranging from cryptography and gambling to numerical simulation of physical and biological systems. Random numbers, however, are difficult to characterize mathematically, and their generation must rely on an unpredictable physical process. Inaccuracies in the theoretical modelling of such processes or failures of the devices, possibly due to adversarial attacks, limit the reliability of random number generators in ways that are difficult to control and detect. Here, inspired by earlier work on non-locality-based and device-independent quantum information processing, we show that the non-local correlations of entangled quantum particles can be used to certify the presence of genuine randomness. It is thereby possible to design a cryptographically secure random number generator that does not require any assumption about the internal working of the device. Such a strong form of randomness generation is impossible classically and possible in quantum systems only if certified by a Bell inequality violation. We carry out a proof-of-concept demonstration of this proposal in a system of two entangled atoms separated by approximately one metre. The observed Bell inequality violation, featuring near perfect detection efficiency, guarantees that 42 new random numbers are generated with 99 per cent confidence. Our results lay the groundwork for future device-independent quantum information experiments and for addressing fundamental issues raised by the intrinsic randomness of quantum theory.

Subfields: Atomic and Molecular Physics, and Optics, Computational Theory and Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/29dd7297102a2f248323aa5450ea7b3980180091

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Citations in the corpus

Quantum random number generation (2015, positive): “Based on the Clauser-Horne-Shimony-Holt (CHSH) inequality 59 , Fehr et al. 62 and Pironio et al. 63 proposed self-testing randomness expansion protocols against classical adversaries.”
Advances in quantum cryptography (2019, positive): “While the first DI-QRE experiment ran at a very low rate [708], recent state-of-the-art experiments achieve reasonable rates [713] and even close the locality loophole as well as the detection loophole.”
A Combinatorial Approach to Nonlocality and Contextuality (2012, background): “Since its discovery, it has found manifold applications in quantum information theory like [78,79].”
Quantum random number generators (2016, methodology): “The protocol in (Pironio et al., 2010) is quadratic: in order to produce n certified random bits it consumes a previously existing random sequence of the order of √ n bits.”
A strong no-go theorem on the Wigner’s friend paradox (2019, neutral): “[38] Pironio, S.”
Free randomness can be amplified (2011, methodology): “It is worth contrasting randomness amplification, as considered here, with randomness expansion, introduced in [22] and further developed in [23, 24].”