Multiparticle entanglement in the Lipkin-Meshkov-Glick model

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 77, Issue 5, 2008, Pages

  Cui, H T ^a  

^a ANYANG NORMAL UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

ANTIFERROMAGNETIC MATERIALS; ELEMENTARY PARTICLES; MAGNETIC ANISOTROPY; MATHEMATICAL MODELS; PARAMETER ESTIMATION; PHASE TRANSITIONS;

FERROMAGNETIC COUPLING; LIPKIN-MESHKOV-GLICK MODELS; MULTIPARTICLE ENTANGLEMENT; QUANTUM PHASE TRANSITIONS;

QUANTUM ENTANGLEMENT;

EID: 43249130120     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.77.052105     Document Type: Article

References (54)

1. J. Preskill, J. Mod. Opt. JMOPEW 0950-0340 10.1080/095003400148097 47, 127 (2000).
2. L. Amico, R. Fazio, A. Osterloh, and V. Vedral, e-print arXiv:quant-ph/0703044, Rev. Mod. Phys.
3. T. Senthil, Proceedings of the Conference on 'Recent Progress in Many-Body Theories,' Santa Fe, New Mexico (USA), Aug 23-27, 2004 (2004)
4. also available at e-print arXiv:cond-mat/0411275.
5. A. Y. Kitaev, Ann. Phys. ANPYA2 0003-3804 10.1016/S0003-4916(02)00018-0 303, 2 (2003)
6. R. Moessner and S. L. Sondhi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.1881 86, 1881 (2001)
7. M. A. Levin and X. G. Wen, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.045110 71, 045110 (2005)
8. P. Fendley and E. Fradkin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.024412 72, 024412 (2005)
9. A. Kitaev and J. Preskill, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.110404 96, 110404 (2006)
10. M. A. Levin and X.-G. Wen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.110405 96, 110405 (2006).
11. A. Osterloh, L. Amico, G. Falci, and R. Fazio, Nature (London) NATUAS 0028-0836 10.1038/416608a 416, 608 (2002).
12. T. J. Osborne and M. A. Nielsen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.032110 66, 032110 (2002).
13. M. F. Yang, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.030302 71, 030302 (R) (2005).
14. M. B. Plenio and S. Virmani, Quantum Inf. Comput. QICUAW 1533-7146 7, 1 (2007).
15. H. J. Briegel and R. Raussendorf, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.910 86, 910 (2001).
16. W. Dur, G. Vidal, and J. I. Cirac, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.62.062314 62, 062314 (2000).
17. T.-C. Wei, D. Das, S. Mukhopadyay, S. Vishveshwara, and P. M. Goldbart, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.060305 71, 060305 (R) (2005)
18. S. J. Gu, G. S. Tian, and H. Q. Lin, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/8/4/061 8, 61 (2006).
19. G. Costantini, P. Facchi, G. Florio, and S. Pascazio, J. Phys. A: Math. Theor. ZZZZZZ 1751-8113 40, 8009 (2007).
20. T. R. de Oliveira, G. Rigolin, and M. C. de Oliveira, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.010305 73, 010305 (R) (2006)
21. T. R. de Oliveira, G. Rigolin, M. C. de Oliveira, and E. Miranda, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.170401 97, 170401 (2006).
22. D. A. Meyer and N. R. Wallach, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1497700 43, 4273 (2002).
23. G. K. Brennen, Quantum Inf. Comput. QICUAW 1533-7146 3, 619 (2003).
24. R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, e-print arXiv:quant-ph/0702225.
25. P. Facchi, G. Florio, and S. Pascazio, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74.042331 74, 042331 (2006).
26. H. J. Lipkin, N. Meshkov, and A. J. Glick, Nucl. Phys. NUPHA7 0029-5582 10.1016/0029-5582(65)90862-X 62, 188 (1965)
27. H. J. Lipkin, N. Meshkov, and A. J. Glick, Nucl. Phys. NUPHA7 0029-5582 10.1016/0029-5582(65)90862-X 62, 199 (1965)
28. H. J. Lipkin, N. Meshkov, and A. J. Glick, Nucl. Phys. NUPHA7 0029-5582 10.1016/0029-5582(65)90862-X 62, 211 (1965).
29. J. Vidal, G. Palacios, and R. Mosseri, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.022107 69, 022107 (2004)
30. J. Vidal, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.062318 73, 062318 (2006).
31. S. Dusuel and J. Vidal, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.237204 93, 237204 (2004)
32. S. Dusuel and J. Vidal, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.224420 71, 224420 (2005).
33. J. Vidal, R. Mosseri, and J. Dukelsky, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.054101 69, 054101 (2004).
34. J. Vidal, G. Palacios, and C. Aslangul, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.062304 70, 062304 (2004).
35. R. G. Unanyan, C. Ionescu, and M. Fleischhauer, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.022326 72, 022326 (2005).
36. J. I. Latorre, R. Orus, E. Rico, and J. Vidal, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.064101 71, 064101 (2005)
37. V. Popkov and M. Salerno, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.012301 71, 012301 (2005).
38. J. Vidal, S. Dusuel, and T. Barthel, J. Stat. Mech. 2007, P01015 (2007). 1742-5468
39. R. Somma, G. Ortiz, H. Barnum, E. Knill, and L. Viola, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.042311 70, 042311 (2004).
40. H. Barnum, E. Knill, G. Ortiz, R. Somma, and L. Viola, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.107902 92, 107902 (2004).
41. F. Pan and J. P. Draayer, Phys. Lett. B PYLBAJ 0370-2693 10.1016/S0370-2693(99)00191-4 451, 1 (1999)
42. J. Links, H.-Q. Zhou, R. H. McKenzie, and M. D. Gould, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/36/19/201 36, R63 (2003)
43. G. Ortiz, R. Somma, J. Dukelsky, and S. Rombouts, Nucl. Phys. B NUPBBO 0550-3213 10.1016/j.nuclphysb.2004.11.008 707, 421 (2005).
44. R. Botet, R. Jullien, and P. Pfeuty, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.49.478 49, 478 (1982)
45. R. Botet and R. Jullien, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.28.3955 28, 3955 (1983).
46. H. T. Cui, K. Li, and X. X. Yi, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2006.08.040 360, 243 (2006).
47. X. Wang and K. Mølmer, Eur. Phys. J. D EPJDF6 1434-6060 10.1007/s10053-002-8844-x 18, 385 (2002).
48. Equation 15 obviously failed to measure the n -party GHZ state since its dependence on M2 and the discontinuity of M has no effect on ME.
49. S. Morrison and A. S. Parkins, e-print arXiv:0711.2325.
50. The continuity of function f (x) is defined as limx→ x0 f (x) -f (x0) =0. First suppose that f (x) is a linear function of the subfunctions gk (x) (k=1,2,...,n), i.e., f (x) = k=1 n ck gk (x) in which ck is the coefficient. Without loss of generality any gk (x) is not supposed to be the linear combination of the other gk (x). Then the continuity of f (x) requires k=0 n ck limx→ x0 gk (x) - gk (x0) =0, limx→ x0 gk (x) - gk (x0) =0. The conclusion above means that the continuity of gk (x) is a sufficient and necessary condition for the continuity of f (x). With respect to the nonlinear case, let us consider the function f [g (x)] for simplicity. From the definition of the continuity and supposing δx=x- x0, it requires limx→ x0 f [g (x)] -f [g (x0)] =0, | limδx→0 (f [g (x)] / x) | x= x0 δx=0, | limδx→0 { f [g (x)] / g (x) } | x= x0 [g (x) -g (x0)] =0. The prefactor | f [g (x)] / g (x) | x= x0 has a nontrivial effect. Even if limδx→0 g (x) -g (x0) 0, the condition of continuity may still be satisfied only if this prefactor vanishes and limδx→0 g (x) -g (x0) keeps finite.
51. I. L. Chuang and Y. Yamamoto, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.4281 76, 4281 (1996)
52. L.-M. Duan and G. C. Guo, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.1953 79, 1953 (1997).
53. Clare Hewitt-Horsman and Vlatko Vedral, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.76.062319 76, 062319 (2007)
54. Clare Hewitt-Horsman and Vlatko Vedral, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/9/5/135 9, 135 (2007).