Nature464, 1021-1024 (15 April 2010) | doi:10.1038/nature09008; Received 25 November 2009; Accepted 18 February 2010
Random numbers certified by Bell’s theorem
S. Pironio1,2,7, A. Acín3,4,7, S. Massar1,7, A. Boyer de la Giroday5, D. N. Matsukevich6, P. Maunz6, S. Olmschenk6, D. Hayes6, L. Luo6, T. A. Manning6 & C. Monroe6
Laboratoire d’Information Quantique, CP 225, Université Libre de Bruxelles, Bvd Du Triomphe, 1050 Bruxelles, Belgium
Group of Applied Physics, University of Geneva, 1211 Geneva, Switzerland
ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
ICREA-Institucio Catalana de Recerca i Estudis Avançats, 08010 Barcelona, Spain
Cavendish Laboratory, Cambridge University, Cambridge CB3 0HE, UK
Joint Quantum Institute, University of Maryland Department of Physics and National Institute of Standards and Technology, College Park, Maryland 20742, USA
These authors contributed equally to this work.
Correspondence to: A. Acín3,4,7 Correspondence and requests for materials should be addressed to A.A. (Email: antonio.acin@icfo.es).
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 mathematically1, and their generation must rely on an unpredictable physical process2, 3, 4, 5, 6. 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-based7, 8, 9 and device-independent10, 11, 12, 13, 14 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 violation15. 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.
