Experimentally generated randomness certified by the impossibility of superluminal signals


From dice to modern electronic circuits, there have been many attempts to build better devices to generate random numbers. Randomness is fundamental to security and cryptographic systems and to safeguarding privacy. A key challenge with random-number generators is that it is hard to ensure that their outputs are unpredictable1,2,3. For a random-number generator based on a physical process, such as a noisy classical system or an elementary quantum measurement, a detailed model that describes the underlying physics is necessary to assert unpredictability. Imperfections in the model compromise the integrity of the device. However, it is possible to exploit the phenomenon of quantum non-locality with a loophole-free Bell test to build a random-number generator that can produce output that is unpredictable to any adversary that is limited only by general physical principles, such as special relativity1,2,3,4,5,6,7,8,9,10,11. With recent technological developments, it is now possible to carry out such a loophole-free Bell test12,13,14,22. Here we present certified randomness obtained from a photonic Bell experiment and extract 1,024 random bits that are uniformly distributed to within 10−12. These random bits could not have been predicted according to any physical theory that prohibits faster-than-light (superluminal) signalling and that allows independent measurement choices. To certify and quantify the randomness, we describe a protocol that is optimized for devices that are characterized by a low per-trial violation of Bell inequalities. Future random-number generators based on loophole-free Bell tests may have a role in increasing the security and trust of our cryptographic systems and infrastructure.

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Fig. 1: Diagram of the experiment.
Fig. 2: Extractable bits as a function of error.


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We thank C. Miller and K. Coakley for comments on the manuscript. A.M. acknowledges financial support through NIST grant 70NANB16H207. This work is a contribution of the National Institute of Standards and Technology and is not subject to US copyright.

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Nature thanks S. Pironio and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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P.B. led the project and implemented the protocol. P.B., E.K., S.G. and Y.Z. developed the protocol theory. A.M., S.J., A.R. and Y.-K.L. were responsible for the extractor theory and implementation. B.C., S.W.N., M.J.S. and L.K.S. collected and interpreted the data. P.B., E.K., S.G. and L.K.S. wrote the manuscript.

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Correspondence to Peter Bierhorst.

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Supplementary Information

This file contains a Supplementary Discussion, Supplementary Tables 1-6, Supplementary Equations and Supplementary References. It includes the proofs of the Entropy Production Theorem and the Protocol Soundness Theorem. It also describes how we choose the Bell function T, the implementation of the randomness extraction algorithm, details of how we analyzed the data, and comparisons to other implementations. It includes six tables S1-S6: S1 “Protocol for randomness generation,” S2 “Result counts,” S3 “Maximum likelihood non-signaling distribution,” S4 “Bell function T” (with legend), S5 “Summary of application of protocol to data sets” (with legend), and S6 “2-tail p-values for consistency checks.”.

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Bierhorst, P., Knill, E., Glancy, S. et al. Experimentally generated randomness certified by the impossibility of superluminal signals. Nature 556, 223–226 (2018). https://doi.org/10.1038/s41586-018-0019-0

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