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Title: Bell inequalities stronger than the Clauser-Horne-Shimony-Holt inequality for three-level isotropic states

Abstract

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.

Authors:
 [1];  [1];  [2]
  1. Department of Computer Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033 (Japan)
  2. School of Computer Science, McGill University, 3480 University Street, Montreal, Quebec H3A 2A7 (Canada)
Publication Date:
OSTI Identifier:
20787069
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 73; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevA.73.042109; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; BELL THEOREM; ENERGY LEVELS; MATHEMATICAL SOLUTIONS; OPTIMIZATION; QUANTUM MECHANICS

Citation Formats

Ito, Tsuyoshi, Imai, Hiroshi, ERATO-SORST Quantum Computation and Information Project, Japan Science and Technology Agency, 5-28-3 Hongo, Bunkyo-ku, Tokyo, 113-0033, and Avis, David. Bell inequalities stronger than the Clauser-Horne-Shimony-Holt inequality for three-level isotropic states. United States: N. p., 2006. Web. doi:10.1103/PHYSREVA.73.0.
Ito, Tsuyoshi, Imai, Hiroshi, ERATO-SORST Quantum Computation and Information Project, Japan Science and Technology Agency, 5-28-3 Hongo, Bunkyo-ku, Tokyo, 113-0033, & Avis, David. Bell inequalities stronger than the Clauser-Horne-Shimony-Holt inequality for three-level isotropic states. United States. https://doi.org/10.1103/PHYSREVA.73.0
Ito, Tsuyoshi, Imai, Hiroshi, ERATO-SORST Quantum Computation and Information Project, Japan Science and Technology Agency, 5-28-3 Hongo, Bunkyo-ku, Tokyo, 113-0033, and Avis, David. 2006. "Bell inequalities stronger than the Clauser-Horne-Shimony-Holt inequality for three-level isotropic states". United States. https://doi.org/10.1103/PHYSREVA.73.0.
@article{osti_20787069,
title = {Bell inequalities stronger than the Clauser-Horne-Shimony-Holt inequality for three-level isotropic states},
author = {Ito, Tsuyoshi and Imai, Hiroshi and ERATO-SORST Quantum Computation and Information Project, Japan Science and Technology Agency, 5-28-3 Hongo, Bunkyo-ku, Tokyo, 113-0033 and Avis, David},
abstractNote = {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.},
doi = {10.1103/PHYSREVA.73.0},
url = {https://www.osti.gov/biblio/20787069}, journal = {Physical Review. A},
issn = {1050-2947},
number = 4,
volume = 73,
place = {United States},
year = {Sat Apr 15 00:00:00 EDT 2006},
month = {Sat Apr 15 00:00:00 EDT 2006}
}