Nonlocality of cluster states of qubits

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 71, Issue 4, 2005, Pages

  Scarani, Valerio ^a   Acín, Antonio ^b   Schenck, Emmanuel ^c   Aspelmeyer, Markus ^c  

^a UNIVERSITY OF GENEVA   (Switzerland)

^b ICFO INSTITUT DE CIENCIES FOTONIQUES   (Spain)

^c INSTITUT FÜR EXPERIMENTALPHYSIK   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

CLUSTER STATES; GREENBERGER-HORNE-ZEILINGER (GHZ); NONLOCALITY; QUBITS;

CRYSTAL LATTICES;

HIGH ENERGY PHYSICS;

EID: 26944471711     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.71.042325     Document Type: Article

References (26)

1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, U.K., 2000).
2. R. Raussendorf and H. J. Briegel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.5188 86, 5188 (2001);
3. R. Raussendorf, D. E. Browne, and H. J. Briegel, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.022312 68, 022312 (2003).
4. T. E. Tessier, I. H. Deutsch, and C. M. Caves, e-print quant-ph/0407133.
5. H. J. Briegel and R. Raussendorf, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.910 86, 910 (2001).
6. F. Verstraete and J. I. Cirac, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.060302 70, 060302 (2004), and references therein.
7. D. Gottesman, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.54.1862 54, 1862 (1996);
8. D. Schlingemann and R. F. Werner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.012308 65, 012308 (2001).
9. Some nonlocality properties of five-qubit states associated with error correction were studied by D. P. DiVincenzo and A. Peres, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.55.4089 55, 4089 (1997). These states are indeed cluster states on a closed five-site loop, because they are eigenstates of Sa=Za b∈neigh(a) Xb on this cluster, as can be seen in Eq. (3) of the paper.
10. D. M. Greenberger, M. Horne, and A. Zeilinger, in Bell's Theorem, Quantum Theory, and Conceptions of the Universe, edited by, E. Kafatos, (Kluwer, Dordrecht, 1989), p. 69;
11. N. D. Mermin, Am. J. Phys. AJPIAS 0002-9505 10.1119/1.16503 58, 731 (1990).
12. N. D. Mermin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.65. 1838 65, 1838 (1990);
13. M. Ardehali, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.46.5375 46, 5375 (1992);
14. A. V. Belinskii and D. N. Klyshko, Phys. Usp. PHUSEY 1063-7869 10.1016/0375-9601(93)90228-R 36, 653 (1993).
15. V. Scarani and N. Gisin, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/ 34/30/314 34, 6043 (2001);
16. M. Żukowski, Č. Brukner, W. Laskowski, and M. Wieśniak, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.210402 88, 210402 (2002).
17. This equivalence, on the classical level, with Mermin's inequality implies in particular that our inequality is "tight," that is, it is a face of the polytope of local probabilities. We have also checked the tightness directly, using the arguments described by L. Masanes, Quantum Inf. Comput. QICUAW 1533-7146 3, 345 (2003).
18. R. F. Werner and M. M. Wolf, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.032112 64, 032112 (2001);
19. M. Żukowski and Č.. Brukner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.210401 88, 210401 (2002).
20. See another inequality for qubits, useful to detect some states, with no local constraints on one particle in X.-H. Wu and H.-S. Zhong, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.032102 68, 032102 (2003).
21. For the inequalities of Ref., the maximal violation is always obtained by the GHZ state. In the case of three qubits (we recall that the cluster state is then the GHZ state) an inequality using two settings per site has been found, which does not detect GHZ entanglement for three qubits: A. Cabello, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.032108 65, 032108 (2002), Eq. (14).
22. The only inequality known so far that detects all pure entangled three-qubit states (J.-L. Chen, C. Wu, L. C. Kwek, and C. H. Oh, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.140407 93, 140407 (2004), is such that the GHZ state does not provide the maximal violation.
23. M. Hein, J. Eisert, and H. J. Briegel, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.062311 69, 062311 (2004).
24. O. Gühne, G. Tóth, P. Hyllus, and H. J. Briegel, e-print quant-ph/0410059
25. M. A. Nielsen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93. 040503 93, 040503 (2004);
26. D. E. Browne and T. Rudolph, e-print quant-ph/0405157.