Coincidence Bell Inequality for Three Three-Dimensional Systems

A. Acín, J. L. Chen, N. Gisin, D. Kaszlikowski, L. C. Kwek, C. H. Oh, and M. Żukowski

Phys. Rev. Lett. 92, 250404 – Published 23 June 2004

Abstract

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.

Received 16 July 2003

DOI:https://doi.org/10.1103/PhysRevLett.92.250404

Authors & Affiliations

A. Acín^1,2, J. L. Chen^3,4, N. Gisin², D. Kaszlikowski^4,5, L. C. Kwek^4,6, 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

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Vol. 92, Iss. 25 — 25 June 2004

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