New classes of facets of the cut polytope and tightness of Imm 22 Bell inequalities

Discrete Applied Mathematics

Volumn 155, Issue 13, 2007, Pages 1689-1699

  Avis, David ^a   Ito, Tsuyoshi ^b  

^a MCGILL UNIVERSITY   (Canada)

^b UNIVERSITY OF TOKYO   (Japan)

Author keywords

Correlation polytope; Cut polytope; Grishukhin inequality; Imm 22 Bell inequality

Indexed keywords

CORRELATION METHODS; PROBLEM SOLVING; QUANTUM COMPUTERS; THEOREM PROVING;

CORRELATION POLYTOPE; CUT POLYTOPE; GRISHUKHIN INEQUALITY; IMM 22 BELL INEQUALITY; QUANTUM INFORMATION THEORY;

GRAPH THEORY;

EID: 34547454283     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2007.03.005     Document Type: Article

References (20)

1. 1 embeddability, complexity and multicommodity flows. Networks 21 (1991) 595-617
2. Avis D., Imai H., and Ito T. Generating facets for the cut polytope of a graph by triangular elimination. Math. Programming (Online First) (2006) 10.1007/s10107-006-0018-z arXiv:math.CO/0601375
3. Avis D., Imai H., Ito T., and Sasaki Y. Two-party Bell inequalities derived from combinatorics via triangular elimination. J. Phys. A 38 50 (2005) 10971-10987 arXiv:quant-ph/0505060
4. Avis D., and Mutt. All the facets of the six point Hamming cone. European J. Combin. 10 (1989) 309-312
5. Bell J.S. On the Einstein Podolsky Rosen paradox. Physics 1 3 (1964) 195-200
6. Clauser J.F., Horne M.A., Shimony A., and Holt R.A. Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23 15 (1969) 880-884
7. Collins D., and Gisin N. A relevant two qubit Bell inequality inequivalent to the CHSH inequality. J. Phys. A 37 5 (2004) 1775-1787 arXiv:quant-ph/0306129
8. De Simone C., Deza M., and Laurent M. Collapsing and lifting for the cut cone. Discrete Math. 127 1-3 (1994) 105-130
9. Deza M., and Laurent M. Applications of cut polyhedra I. J. Comput. Appl. Math. 55 2 (1994) 191-216
10. Deza M., and Laurent M. Applications of cut polyhedra II. J. Comput. Appl. Math. 55 2 (1994) 217-247
11. M.M. Deza, M. Laurent, Geometry of Cuts and Metrics, Algorithms and Combinatorics, vol. 15, Springer, Berlin, May 1997.
12. Fine A. Hidden variables, joint probability, and the Bell inequalities. Phys. Rev. Lett. 48 5 (1982) 291-295
13. n for n = 7 are known. European J. Combin. 11 (1990) 115-117
14. T. Ito, Y. Sasaki, H. Imai, D. Avis, Families of tight Bell inequalities derived from classes of facets of cut polytopes, in: Proceedings of ERATO Conference on Quantum Information Science (EQIS'04), September 2004, pp. 78-79.
15. O. Krüger, R.F. Werner, Some open problems in quantum information theory, arXiv:quant-ph/0504166, April 2005, See also 〈http://www.imaph.tu-bs.de/qi/problems/problems.html〉.
16. Pitowsky I. Quantum Probability-Quantum Logic, Lecture Notes in Physics vol. 321 (1989), Springer, Berlin
17. Pitowsky I. Correlation polytopes: their geometry and complexity. Math. Programming 50 (1991) 395-414
18. Pitowsky I., and Svozil K. Optimal tests of quantum nonlocality. Phys. Rev. A 64 014102 (2001) arXiv:quant-ph/0011060
19. Tylkin M.E. On Hamming geometry of unitary cubes. Dokl. Akad. Nauk SSSR 134 (1960) 1037-1040 (in Russian; English translation in: Cybernet. and Control Theory 134(5) (1961) 940-943)
20. Werner R.F., and Wolf M.M. Bell inequalities and entanglement. Quantum Inform. Comput. 1 3 (2001) 1-25 arXiv:quant-ph/0107093