Bound entanglement in quantum phase transitions

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 81, Issue 4, 2010, Pages

  Baghbanzadeh, S ^a   Alipour, S ^a   Rezakhani, A T ^b  

^a SHARIF UNIVERSITY OF TECHNOLOGY   (Iran)

^b UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUND ENTANGLEMENT; DENSITY MATRIX; ENTANGLEMENT PROPERTIES; LAY-OUT; PURE STATE; QUANTUM CRITICALITY; QUANTUM PHASE TRANSITIONS; QUANTUM SPIN; WHOLE SYSTEMS;

HAMILTONIANS; PHASE TRANSITIONS;

QUANTUM ENTANGLEMENT;

EID: 77950499406     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.81.042302     Document Type: Article

References (55)

1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2000).
2. L. Amico, R. Fazio, A. Osterloh, and V. Vedral, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.80.517 80, 517 (2008).
3. S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, England, 1999).
4. P. Zanardi, P. Giorda, and M. Cozzini, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.100603 99, 100603 (2007);
5. A. T. Rezakhani, W.-J. Kuo, A. Hamma, D. A. Lidar, and P. Zanardi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.080502 103, 080502 (2009).
6. A. Osterloh, L. Amico, G. Falci, and R. Fazio, Nature (London) NATUAS 0028-0836 10.1038/416608a 416, 608 (2002).
7. L.-A. Wu, M. S. Sarandy, and D. A. Lidar, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.250404 93, 250404 (2004).
8. L.-A. Wu, M. S. Sarandy, D. A. Lidar, and L. J. Sham, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74.052335 74, 052335 (2006).
9. M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.5239 80, 5239 (1998).
10. R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.81.865 81, 865 (2009).
11. X.-G. Wen and Q. Niu, Phys. Rev. B RMPHAT 1098-0121 10.1103/PhysRevB.41. 9377 41, 9377 (1990);
12. A. Y. Kitaev, Ann. Phys. (NY) APNYA6 0003-4916 10.1016/S0003-4916(02) 00018-0 303, 2 (2003).
13. M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.60.1888 60, 1888 (1999).
14. G. Alber, T. Beth, M. Horodecki, P. Horodecki, R. Horodecki, M. Röttler, H. Weinfurter, R. F. Werner, and A. Zeilinger, Quantum Information: An Introduction to Basic Theoretical Concepts and Experiments, Springer Tracts in Modern Physics, Vol. 173 (Springer, New York, 2001).
15. M. Horodecki and P. Horodecki, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.59.4206 59, 4206 (1999);
16. D. P. DiVincenzo, P. W. Shor, J. A. Smolin, B. M. Terhal, and A. V. Thapliyal, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.61.062312 61, 062312 (2000);
17. W. Dür, J. I. Cirac, M. Lewenstein, and D. Bruß, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.61.062313 61, 062313 (2000);
18. Ł. Pankowski, M. Piani, M. Horodecki, and P. Horodecki, e-print arXiv: 0711.2613.
19. K. Horodecki, M. Horodecki, P. Horodecki, and J. Oppenheim, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.160502 94, 160502 (2005).
20. P. Horodecki, M. Horodecki, and R. Horodecki, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.1056 82, 1056 (1999);
21. L. Masanes, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96. 150501 96, 150501 (2006).
22. J. Oppenheim, M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.180402 89, 180402 (2002).
23. M. Piani and J. Watrous, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.250501 102, 250501 (2009).
24. A. Ferraro, D. Cavalcanti, A. García-Saez, and A. Acín, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.080502 100, 080502 (2008).
25. D. Patané, R. Fazio, and L. Amico, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/9/9/322 9, 322 (2007).
26. E. Amselem and M. Bourennane, Nature Phys. NJOPFM 1745-2473 10.1038/nphys1372 5, 748 (2009).
27. G. Vidal and R. F. Werner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.032314 65, 032314 (2002).
28. O. Rudolph, Quantum Inf. Process 1570-0755 10.1007/s11128-005-5664-1 4, 219 (2005);
29. K. Chen and L.-A. Wu, Quantum Inf. Comput. 3, 193 (2003).
30. L. Clarisse and P. Wocjan, Quantum Inf. Comput. 6, 277 (2006).
31. G. Tóth, Ch. Knapp, O. Gühne, and H. J. Briegel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.250405 99, 250405 (2007).
32. P. Zanardi and N. Paunković, Phys. Rev. E PRLTAO 1539-3755 10.1103/PhysRevE.74.031123 74, 031123 (2006);
33. M. Cozzini, R. Ionicioiu, and P. Zanardi, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.76.104420 76, 104420 (2007).
34. W.-L. You, Y.-W. Li, and S.-J. Gu, Phys. Rev. E PRLTAO 1539-3755 10.1103/PhysRevE.76.022101 76, 022101 (2007);
35. S.-J. Gu, H.-M. Kwok, W.-Q. Ning, and H.-Q. Lin, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.77.245109 77, 245109 (2008).
36. S.-J. Gu, e-print arXiv: 0811.3127.
37. J. Kempe, A. Kitaev, and O. Regev, SIAM J. Comput. SMJCAT 0097-5397 10.1137/S0097539704445226 35, 1070 (2004);
38. S. P. Jordan and E. Farhi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.062329 77, 062329 (2008).
39. S. Alipour, S. Baghbanzadeh, and V. Karimipour, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/84/67006 84, 67006 (2008).
40. R. F. Werner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.40.4277 40, 4277 (1989).
41. S. Alipour, V. Karimipour, and L. Memarzadeh, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.052322 75, 052322 (2007).
42. N. Paunković, P. D. Sacramento, P. Nogueira, V. R. Vieira, and V. K. Dugaev, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.052302 77, 052302 (2008).
43. E. Eriksson and H. Johannesson, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.060301 79, 060301 (R) (2009).
44. K. Chen, S. Albeverio, and S.-M. Fei, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.040504 95, 040504 (2005).
45. J. Cai and W. Song, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.101.190503 101, 190503 (2008).
46. C.-J. Zhang, Y.-S. Zhang, S. Zhang, and G.-C. Guo, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.060301 77, 060301 (R) (2008).
47. P. Horodecki, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(97)00416- 7 232, 333 (1997).
48. S. L. Woronowicz, Rep. Math. Phys. RMHPBE 0034-4877 10.1016/0034-4877(76) 90038-0 10, 165 (1976).
49. R. A. Bertlmann and Ph. Krammer, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.024303 77, 024303 (2008).
50. E. Størmer, Proc. Am. Math. Soc. PAMYAR 0002-9939 10.2307/2044436 86, 402 (1982);
51. P. Horodecki, M. Horodecki, and R. Horodecki, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.1056 82, 1056 (1999).
52. L. D. Faddeev, Sov. Sci. Rev., Sect. C, Math. Phys. Rev. C 1, 107 (1981).
53. K. Horodecki, L. Pankowski, M. Horodecki, and P. Horodecki, IEEE Trans. Quantum Inf. Theo. IETTAW 0018-9448 10.1109/TIT.2008.921709 54, 2621 (2008).
54. G. Smith and J. Yard, Science SCIEAS 0036-8075 10.1126/science.1162242 321, 1812 (2008).
55. V. S. Malinovsky and I. R. Sola, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.190502 93, 190502 (2004).