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Phys. Rev. Lett. 92, 250404 (2004) [4 pages]

Coincidence Bell Inequality for Three Three-Dimensional Systems

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A. Acín1,2, J. L. Chen3,4, N. Gisin2, D. Kaszlikowski4,5, L. C. Kwek4,6, C. H. Oh4, and M. Żukowski5
1Institut de Ciències Fotòniques, Jordi Girona 29, Edifici Nexus II, 08034 Barcelona, Spain
2GAP-Optique, University of Geneva, 20, Rue de l’École de Médecine, CH-1211 Geneva 4, Switzerland
3Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009(26), Beijing 100088, People’s Republic of China
4Department of Physics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260
5Instytut Fizyki Teoretycznej i Astrofizyki, Uniwersytet Gdański, PL-80-952, Gdańsk, Poland
6National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore 639798

Received 16 July 2003; published 23 June 2004

We construct a Bell inequality for coincidence probabilities on a three three-dimensional (qutrit) system. We show that this inequality is violated when each observer measures two noncommuting observables, defined by the so-called unbiased six-port beam splitter, on a maximally entangled state of two qutrits. The strength of the violation agrees with the numerical results presented by Kaszlikowski et al. , quant-ph/0202019. It is proven that the inequality defines facets of the polytope of local variable models.

© 2004 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.92.250404
DOI:
10.1103/PhysRevLett.92.250404
PACS:
03.65.Ud, 03.67.Mn
 
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