Skip to main content
SpringerLink
Log in

Time-invariant entanglement and sudden death of nonlocality for multipartite systems under collective dephasing

  • Regular Article
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

We investigate the dynamics of entanglement and nonlocality for multipartite quantum systems under collective dephasing. Using an exact and computable measure for genuine entanglement, we demonstrate the possibility of a non trivial phenomenon of time-invariant entanglement for multipartite quantum systems. We find that for four qubits, there exist quantum states, which are changing continously nevertheless their genuine entanglement remains constant. Based on our numerical results, we conjecture that there is no evidence of time-invariant entanglement for quantum states of three qubits. We point out that quantum states exhibiting time-invariant entanglement must live in both decoherence free subspace and in the subspaces orthogonal to it. The previous studies on this feature for two qubits can be recovered from our studies as a special case. We also study the nonlocality of quantum states under collective dephasing. We find that although genuine entanglement of quantum states may not change, however their nonlocality changes. We discuss the possibility of finite time end of genuine nonlocality.

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki, Rev. Mod. Phys. 81, 865 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  2. O. Gühne, G. Tóth, Phys. Rep. 474, 1 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  3. N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, S. Wehner, Rev. Mod. Phys. 86, 419 (2014)

    Article  ADS  Google Scholar 

  4. L. Aolita, F. de Melo, L. Davidovich, Rep. Prog. Phys. 78, 042001 (2015)

    Article  ADS  Google Scholar 

  5. T. Yu, J.H. Eberly, Phys. Rev. Lett. 93, 140404 (2004)

    Article  ADS  Google Scholar 

  6. W. Dür, H.J. Briegel, Phys. Rev. Lett. 92, 180403 (2002)

    Article  Google Scholar 

  7. M. Hein, W. Dür, H.J. Briegel, Phys. Rev. A 71, 032350 (2005)

    Article  ADS  Google Scholar 

  8. L. Aolita, R. Chaves, D. Cavalcanti, A. Acín, L. Davidovich, Phys. Rev. Lett. 100, 080501 (2008)

    Article  ADS  Google Scholar 

  9. C. Simon, J. Kempe, Phys. Rev. A 65, 052327 (2002)

    Article  ADS  Google Scholar 

  10. A. Borras, A.P. Majtey, A.R. Plastino, M. Casas, A. Plastino, Phys. Rev. A 79, 022108 (2009)

    Article  ADS  Google Scholar 

  11. D. Cavalcanti, R. Chaves, L. Aolita, L. Davidovich, A. Acín, Phys. Rev. Lett. 103, 030502 (2009)

    Article  ADS  Google Scholar 

  12. S. Bandyopadhyay, D.A. Lidar, Phys. Rev. A 72, 042339 (2005)

    Article  ADS  Google Scholar 

  13. R. Chaves, L. Davidovich, Phys. Rev. A 82, 052308 (2010)

    Article  ADS  Google Scholar 

  14. L. Aolita, D. Cavalcanti, R. Chaves, C. Dhara, L. Davidovich, A. Acín, Phys. Rev. A 82, 032317 (2010)

    Article  ADS  Google Scholar 

  15. A.R.R. Carvalho, F. Mintert, A. Buchleitner, Phys. Rev. Lett. 93, 230501 (2004)

    Article  ADS  Google Scholar 

  16. F. Lastra, G. Romero, C.E. López, M. França Santos, J.C. Retamal, Phys. Rev. A 75, 062324 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  17. O. Gühne, F. Bodoky, M. Blaauboer, Phys. Rev. A 78, 060301(R) (2008)

    Article  Google Scholar 

  18. C.E. López, G. Romero, F. Lastra, E. Solano, J.C. Retamal, Phys. Rev. Lett. 101, 080503 (2008)

    Article  Google Scholar 

  19. A.R.P. Rau, M. Ali, G. Alber, Europhys. Lett. 82, 40002 (2008)

    Article  ADS  Google Scholar 

  20. M. Ali, G. Alber, A.R.P. Rau, J. Phys. B 42, 025501 (2009)

    Article  ADS  Google Scholar 

  21. M. Ali, J. Phys. B 43, 045504 (2010)

    Article  ADS  Google Scholar 

  22. Y.S. Weinstein, J. Feldman, J. Robins, J. Zukus, G. Gilbert, Phys. Rev. A 85, 032324 (2012)

    Article  ADS  Google Scholar 

  23. S.N. Filippov, A.A. Melnikov, M. Ziman, Phys. Rev. A 88, 062328 (2013)

    Article  ADS  Google Scholar 

  24. M. Ali, O. Gühne, J. Phys. B 47, 055503 (2014)

    Article  ADS  Google Scholar 

  25. M. Ali, Phys. Lett. A 378, 2048 (2014)

    Article  ADS  Google Scholar 

  26. M. Ali, A.R.P. Rau, Phys. Rev. A 90, 042330 (2014)

    Article  ADS  Google Scholar 

  27. M. Ali, Open. Sys. Info. Dyn. 21, 1450008 (2014)

    Article  Google Scholar 

  28. T. Yu, J.H. Eberly, Phys. Rev. B 66, 193306 (2002)

    Article  ADS  Google Scholar 

  29. T. Yu, J.H. Eberly, Phys. Rev. B 68, 165322 (2003)

    Article  ADS  Google Scholar 

  30. T. Yu, J.H. Eberly, Opt. Commun. 264, 393 (2006)

    Article  ADS  Google Scholar 

  31. G. Jaeger, K. Ann, J. Mod. Opt. 54, 2327 (2007)

    Article  Google Scholar 

  32. S.-B. Li, J.-B. Xu, Eur. Phys. J. D 41, 377 (2007)

    Article  ADS  Google Scholar 

  33. G. Karpat, Z. Gedik, Phys. Lett. A 375, 4166 (2011)

    Article  ADS  Google Scholar 

  34. M. Ali, Phys. Rev. A 81, 042303 (2010)

    Article  ADS  Google Scholar 

  35. M. Ali, Chin. Phys. Lett. 32, 060302 (2015)

    Article  ADS  Google Scholar 

  36. B.H. Liu, X.-M. Hu, J.-S. Chen, C. Zhang, Y.-F. Huang, C.-F. Li, G.-C. Guo, G. Karpat, F.F. Fanchini, J. Piilo, S. Maniscalco, arXiv:1603.09119

  37. E.G. Carnio, A. Buchleitner, M. Gessner, Phys. Rev. Lett. 115, 010404 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  38. E.G. Carnio, A. Buchleitner, M. Gessner, New. J. Phys. 18, 073010 (2016)

    Article  ADS  Google Scholar 

  39. M. Ali, Preprint (2016)

  40. B. Jungnitsch, T. Moroder, O. Gühne, Phys. Rev. Lett. 106, 190502 (2011)

    Article  ADS  Google Scholar 

  41. L. Novo, T. Moroder, O. Gühne, Phys. Rev. A 88, 012305 (2013)

    Article  ADS  Google Scholar 

  42. M. Hofmann, T. Moroder, O. Gühne, J. Phys. A: Math. Theor. 47, 155301 (2014)

    Article  ADS  Google Scholar 

  43. J.S. Bell, Physics 1, 195 (1964)

    Google Scholar 

  44. N. Gisin, Phys. Lett. A 154, 201 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  45. R.F. Werner, Phys. Rev. A 40, 4277 (1989)

    Article  ADS  Google Scholar 

  46. Y.-C. Liang, L. Masanes, D. Rosset, Phys. Rev. A 86, 052115 (2011)

    Article  ADS  Google Scholar 

  47. J.F. Clauser, M.A. Horne, A. Shimony, R.A. Holt, Phys. Rev. Lett. 23, 880 (1969)

    Article  ADS  Google Scholar 

  48. L. Mazzola, B. Bellomo, R. Lo Franco, G. Compagno, Phys. Rev. A 81, 052116 (2010)

    Article  ADS  Google Scholar 

  49. J.S. Xu, C.-F. Li, M. Gong, X.-B. Zou, C.-H. Shi, G. Chen, G.-C. Guo, Phys. Rev. Lett. 104, 100502 (2010)

    Article  ADS  Google Scholar 

  50. W. Laskowski, T. Paterek, Č. Brukner, M. Żukowski, Phys. Rev. A 81, 042101 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  51. R. Chaves, D. Cavalcanti, L. Aolita, A. Acín, Phys. Rev. A 86, 012108 (2012)

    Article  ADS  Google Scholar 

  52. R. Chaves, A. Acín, L. Aolita, D. Cavalcanti, Phys. Rev. A 89, 042106 (2014)

    Article  ADS  Google Scholar 

  53. A. Sohbi, I. Zaquine, E. Diamanti, D. Markham, Phys. Rev. A 91, 022101 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  54. P. Divianszky, R. Trencsenyi, E. Bene, T. Vertesi, Phys. Rev. A 93, 042113 (2016)

    Article  ADS  Google Scholar 

  55. W. Laskowski, T. Vertesi, M. Wiesniak, J. Phys. A: Math. Theor. 48, 465301 (2015)

    Article  ADS  Google Scholar 

  56. D. Mermin, Phys. Rev. Lett. 65, 1838 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  57. M. Ardehali, Phys. Rev. A 46, 5375 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  58. D. Collins, N. Gisin, S. Popescu, D. Roberts, V. Scarani, Phys. Rev. Lett. 88, 170405 (2002)

    Article  ADS  Google Scholar 

  59. J.-D. Bancal, N. Brunner, N. Gisin, Y.-C. Liang, Phys. Rev. Lett. 106, 020405 (2011)

    Article  ADS  Google Scholar 

  60. G. Svetlichny, Phys. Rev. D 35, 3066 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  61. J.-W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, A. Zeilinger, Nature 403, 515 (2000)

    Article  ADS  Google Scholar 

  62. J. Lavoie, R. Kaltenbaek, K.J. Resch, New. J. Phys. 11, 073051 (2009)

    Article  ADS  Google Scholar 

  63. C. Erven, E. Meyer-Scott, K. Fisher, J. Lavoie, B.L. Higgins, Z. Yan, C.J. Pugh, J.-P. Bourgoin, R. Prevedel, L.K. Shalm, L. Richards, N. Gigov, R. Laflamme, G. Weihs, T. Jennewein, K.J. Resch, Nat. Photon. 8, 292 (2014)

    Article  ADS  Google Scholar 

  64. B. Jungnitsch, S. Niekamp, M. Kleinmann, O. Gühne, H. Lu, W.-B. Gao, Y.-A. Chen, Z.-B. Chen, J.-W. Pan, Phys. Rev. Lett. 104, 210401 (2010)

    Article  ADS  Google Scholar 

  65. A. Peres, Phys. Rev. Lett. 77, 1413 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  66. L. Vandenberghe, S. Boyd, SIAM Rev. 38, 49 (1996)

    Article  MathSciNet  Google Scholar 

  67. G. Vidal, R.F. Werner, Phys. Rev. A 65, 032314 (2002)

    Article  ADS  Google Scholar 

  68. B. Jungnitsch, T. Moroder, O. Gühne, Phys. Rev. A 84, 032310 (2011)

    Article  ADS  Google Scholar 

  69. C. Sabín, G. García-Alcaine, Eur. Phys. J. D 48, 435 (2008)

    Article  ADS  Google Scholar 

  70. P. Schindler, D. Nigg, T. Monz, J.T. Barreiro, E. Martinez, S.X. Wang, S. Quint, M.F. Brandl, V. Nebendahl, C.F. Roos, M. Chwalla, M. Hennrich, R. Blatt, New. J. Phys. 15, 123012 (2013)

    Article  ADS  Google Scholar 

  71. B.P. Lanyon, P. Jurcevic, C. Hempel, M. Gessner, V. Vedral, R. Blatt, C.F. Roos, Phys. Rev. Lett. 111, 100504 (2013)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Faculty of Engineering, Islamic University Madinah, 107, Madinah, Saudi Arabia

    Mazhar Ali

Authors
  1. Mazhar Ali
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mazhar Ali.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ali, M. Time-invariant entanglement and sudden death of nonlocality for multipartite systems under collective dephasing. Eur. Phys. J. D 71, 1 (2017). https://doi.org/10.1140/epjd/e2016-70680-8

Download citation

  • Received:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/e2016-70680-8

Keywords

Search

Navigation