Bell inequalities stronger than the Clauser-Horne-Shimony-Holt inequality for three-level isotropic states
- Department of Computer Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033 (Japan)
- School of Computer Science, McGill University, 3480 University Street, Montreal, Quebec H3A 2A7 (Canada)
We show that some two-party Bell inequalities with two-valued observables are stronger than the CHSH inequality for 3x3 isotropic states in the sense that they are violated by some isotropic states in the 3x3 system that do not violate the CHSH inequality. These Bell inequalities are obtained by applying triangular elimination to the list of known facet inequalities of the cut polytope on nine points. This gives a partial solution to an open problem posed by Collins and Gisin. The results of numerical optimization suggest that they are candidates for being stronger than the I{sub 3322} Bell inequality for 3x3 isotropic states. On the other hand, we found no Bell inequalities stronger than the CHSH inequality for 2x2 isotropic states. In addition, we illustrate an inclusion relation among some Bell inequalities derived by triangular elimination.
- OSTI ID:
- 20787069
- Journal Information:
- Physical Review. A, Vol. 73, Issue 4; Other Information: DOI: 10.1103/PhysRevA.73.042109; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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