Local realism is the idea that objects have definite properties whether or not they are measured, and that measurements of these properties are not affected by events taking place sufficiently far away1. Einstein, Podolsky and Rosen2 used these reasonable assumptions to conclude that quantum mechanics is incomplete. Starting in 1965, Bell and others constructed mathematical inequalities whereby experimental tests could distinguish between quantum mechanics and local realistic theories1,3,4,5. Many experiments1,6,7,8,9,10,11,12,13,14,15 have since been done that are consistent with quantum mechanics and inconsistent with local realism. But these conclusions remain the subject of considerable interest and debate, and experiments are still being refined to overcome ‘loopholes’ that might allow a local realistic interpretation. Here we have measured correlations in the classical properties of massive entangled particles (9Be+ ions): these correlations violate a form of Bell's inequality. Our measured value of the appropriate Bell's ‘signal’ is 2.25 ± 0.03, whereas a value of 2 is the maximum allowed by local realistic theories of nature. In contrast to previous measurements with massive particles, this violation of Bell's inequality was obtained by use of a complete set of measurements. Moreover, the high detection efficiency of our apparatus eliminates the so-called ‘detection’ loophole.
Subscribe to Journal
Get full journal access for 1 year
only $3.83 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
Clauser, J. F. & Shimony, A. Bell's theorem: experimental tests and implications. Rep. Prog. Phys. 41, 1883–1927 (1978).
Einstein, A., Podolsky, B. & Rosen, N. Can quantum-mechanical description of reality be considered complete? Phys. Rev. 47, 777–780 (1935).
Bell, J. S. On the Einstein-Podolsky-Rosen paradox. Physics 1, 195–200 (1965).
Bell, J. S. in Foundations of Quantum Mechanics (ed. d'Espagnat, B.) 171–181 (Academic, New York, 1971).
Clauser, J. F., Horne, M. A., Shimony, A. & Holt, R. A. Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880–884 (1969).
Freedman, S. J. & Clauser, J. F. Experimental test of local hidden-variable theories. Phys. Rev. Lett. 28, 938–941 (1972).
Fry, E. S. & Thompson, R. C. Experimental test of local hidden-variable theories. Phys. Rev. Lett. 37, 465–468 (1976).
Aspect, A., Grangier, P. & Roger, G. Experimental realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: a new violation of Bell's inequalities. Phys. Rev. Lett. 49, 91–94 (1982).
Aspect, A., Dalibard, J. & Roger, G. Experimental test of Bell's inequalities using time-varying analyzers. Phys. Rev. Lett. 49, 1804–1807 (1982).
Ou, Z. Y. & Mandel, L. Violation of Bell's inequality and classical probability in a two-photon correlation experiment. Phys. Rev. Lett. 61, 50–53 (1988).
Shih, Y. H. & Alley, C. O. New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion. Phys. Rev. Lett. 61, 2921–2924 (1988).
Tapster, P. R., Rarity, J. G. & Owens, P. C. M. Violation of Bell's inequality over 4 km of optical fiber. Phys. Rev. Lett. 73, 1923–1926 (1994).
Kwiat, P. G., Mattle, K., Weinfurter, H. & Zeilinger, A. New high-intensity source of polarization-entangled photon pairs. Phys. Rev. Lett. 75, 4337–4341 (1995).
Tittel, W., Brendel, J., Zbinden, H. & Gisin, N. Violation of Bell inequalities by photons more than 10 km apart. Phys. Rev. Lett. 81, 3563–3566 (1998).
Weihs, G. et al. Violation of Bell's inequality under strict Einstein locality conditions. Phys. Rev. Lett. 81, 5039–5043 (1998).
Aspect, A. Bell's inequality test: more ideal than ever. Nature 398, 189–190 (1999).
Gisin, N. & Zbinden, H. Bell inequality and the locality loophole: active versus passive switches. Phys. Lett. A 264, 103–107 (1999).
Lo, T. K. & Shimony, A. Proposed molecular test of local hidden-variable theories. Phys. Rev. A 23, 3003–3012 (1981).
Kwiat, P. G., Eberhard, P. H., Steinberg, A. M. & Chiao, R. Y. Proposal for a loophole-free Bell inequality experiment. Phys. Rev. A 49, 3209–3220 (1994).
Huelga, S. F., Ferrero, M. & Santos, E. Loophole-free test of the Bell inequality. Phys. Rev. A 51, 5008–5011 (1995).
Fry, E. S., Walther, T. & Li, S. Proposal for a loophole free test of the Bell inequalities. Phys. Rev. A 52, 4381–4395 (1995).
Freyberger, M., Aravind, P. K., Horne, M. A. & Shimony, A. Proposed test of Bell's inequality without a detection loophole by using entangled Rydberg atoms. Phys. Rev. A 53, 1232–1244 (1996).
Brif, C. & Mann, A. Testing Bell's inequality with two-level atoms via population spectroscopy. Europhys. Lett. 49, 1–7 (2000).
Beige, A., Munro, W. J. & Knight, P. L. A Bell's inequality test with entangled atoms. Phys. Rev. A 62, 052102-1–052102-9 (2000).
Lamehi-Rachti, M. & Mittig, W. Quantum mechanics and hidden variables: a test of Bell's inequality by the measurement of the spin correlation in low-energy proton–proton scattering. Phys. Rev. D 14, 2543–2555 (1976).
Hagley, E. et al. Generation of Einstein-Podolsky-Rosen pairs of atoms. Phys. Rev. Lett. 79, 1–5 (1997).
Sackett, C. A. et al. Experimental entanglement of four particles. Nature 404, 256–259 (2000).
Feynman, R. P., Vernon, F. L. & Hellwarth, R. W. Geometrical representation of the Schrödinger equation for solving maser problems. J. Appl. Phys. 28, 49–52 (1957).
Richter, T. Cooperative resonance fluorescence from two atoms experiencing different driving fields. Optica Acta 30, 1769–1780 (1983).
Eichmann, U. et al. Young's interference experiment with light scattered from two atoms. Phys. Rev. Lett. 70, 2359–2362 (1993).
We thank A. Ben-Kish, J. Bollinger, J. Britton, N. Gisin, P. Knight, P. Kwiat and I. Percival for useful discussions and comments on the manuscript. This work was supported by the US National Security Agency (NSA) and the Advanced Research and Development Activity (ARDA), the US Office of Naval Research, and the US Army Research Office. This paper is a contribution of the National Institute of Standards and Technology and is not subject to US copyright.
About this article
Cite this article
Rowe, M., Kielpinski, D., Meyer, V. et al. Experimental violation of a Bell's inequality with efficient detection. Nature 409, 791–794 (2001) doi:10.1038/35057215
Physical Review A (2020)
Physical Review A (2019)
Tripartite entanglement and non-locality in three-qubit Greenberger–Horne–Zeilinger states with bit-flip noise
Canadian Journal of Physics (2019)
International Journal of Quantum Information (2019)
Unified treatment of the total angular momentum of single photons via generalized quantum observables
New Journal of Physics (2019)