Research PapersNo Access

Freezing dynamics of entanglement and nonlocality for qutrit-qutrit (3 ⊗ 3) quantum systems

Mazhar Ali

Mazhar Ali

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

E-mail Address: mazharaliawan@yahoo.com

E-mail Address: mazhar.ali@iu.edu.sa

Search for more papers by this author

https://doi.org/10.1142/S0217732319501025Cited by:1 (Source: Crossref)

Abstract

We examine the possibilities of nontrivial phenomena of time-invariant entanglement and freezing dynamics of entanglement for qutrit-qutrit quantum systems. We find no evidence for time-invariant entanglement, however, we do observe that certain quantum states freeze their entanglement after decaying for some time. It is interesting that quantum states are changing whereas their entanglement remains constant. We find that the combined action of decoherence free subspaces and subspaces where quantum states decay, facilitate this phenomenon. This study is an extension of similar phenomena observed for qubit-qubit systems, qubit-qutrit, and multipartite quantum systems. We examine nonlocality of a specific family of states and find the certain instances where the states still remain entangled, however, they can either loose their nonlocality at a finite time or remain nonlocal for all times.

Keywords:

PACS: 03.65.Yz, 03.65.Ud, 03.67.Mn

References

1. R. Horodecki et al., Rev. Mod. Phys. 81, 865 (2009). Crossref, Web of Science, ADS, Google Scholar
2. O. Gühne and G. Tóth, Phys. Rep. 474, 1 (2009). Crossref, Web of Science, ADS, Google Scholar
3. L. Aolita, F. de Melo and L. Davidovich, Rep. Prog. Phys. 78, 042001 (2015). Crossref, Web of Science, Google Scholar
4. T. Yu and J. H. Eberly, Phys. Rev. B 66, 193306 (2002); 68, 165322 (2003); 93, 140404 (2004). Google Scholar
5. W. Dür and H. J. Briegel, Phys. Rev. Lett. 92, 180403 (2004); M. Hein, W. Dür and H.-J. Briegel, Phys. Rev. A 71, 032350 (2005). Google Scholar
6. L. Aolita et al., Phys. Rev. Lett. 100, 080501 (2008). Crossref, Web of Science, ADS, Google Scholar
7. C. Simon and J. Kempe, Phys. Rev. A 65, 052327 (2002); A. Borras et al., ibid. 79, 022108 (2009); D. Cavalcanti et al., Phys. Rev. Lett. 103, 030502 (2009). Google Scholar
8. S. Bandyopadhyay and D. A. Lidar, Phys. Rev. A 72, 042339 (2005); R. Chaves and L. Davidovich, Phys. Rev. A 82, 052308 (2010); L. Aolita et al., ibid. 82, 032317 (2010). Google Scholar
9. A. R. R. Carvalho, F. Mintert and A. Buchleitner, Phys. Rev. Lett. 93, 230501 (2004). Crossref, Web of Science, ADS, Google Scholar
10. F. Lastra, G. Romero, C. E. Lopez, M. França Santos and J. C. Retamal, Phys. Rev A 75, 062324 (2007). Crossref, Web of Science, ADS, Google Scholar
11. O. Gühne, F. Bodoky and M. Blaauboer, Phys. Rev. A 78, 060301(R) (2008). Crossref, Web of Science, ADS, Google Scholar
12. C. E. López, G. Romero, F. Lastra, E. Solano and J. C. Retamal, Phys. Rev. Lett. 101, 080503 (2008). Crossref, Web of Science, ADS, Google Scholar
13. A. R. P. Rau, M. Ali and G. Alber, EPL 82, 40002 (2008); M. Ali, G. Alber and A. R. P. Rau, J. Phys. B: At. Mol. Opt. 42, 025501 (2009); M. Ali, ibid. 43, 045504 (2010). Google Scholar
14. Y. S. Weinstein et al., Phys. Rev. A 85, 032324 (2012); S. N. Filippov, A. A. Melnikov and M. Ziman, ibid. 88, 062328 (2013). Google Scholar
15. M. Ali and O. Gühne, J. Phys. B: At. Mol. Opt. 47, 055503 (2014); M. Ali, Phys. Lett. A 378, 2048 (2014); M. Ali and A. R. P. Rau, ibid. 90, 042330 (2014); M. Ali, Open. Sys. Inf. Dyn. 21, 1450008 (2014). Google Scholar
16. M. Ali, Chinese Phys. B 24, 120303 (2015); M. Ali, ibid. 32, 060302 (2015). Google Scholar
17. M. Ali, Int. J. Quant. Inf. 14, 1650039 (2016). Link, Web of Science, Google Scholar
18. M. Ali, Int. J. Quant. Inf. 15, 1750022 (2017); M. Ali, Eur. Phys. J. D 71, 1 (2017). Google Scholar
19. T. Yu and J. H. Eberly, Phys. Rev. B 66, 193306 (2002); 68, 165322 (2003); T. Yu and J. H. Eberly, Opt. Commun. 264, 393 (2006). Google Scholar
20. G. Jaeger and K. Ann, J. Mod. Opt. 54, 2327 (2007). Crossref, Web of Science, ADS, Google Scholar
21. S.-B. Li and J.-B. Xu, Eur. Phys. J. D 41, 377 (2007). Crossref, Web of Science, ADS, Google Scholar
22. G. Karpat and Z. Gedik, Phys. Lett. A 375, 4166 (2011). Crossref, Web of Science, ADS, Google Scholar
23. B.-H. Liu et al., Phys. Rev. A 94, 062107 (2016). Crossref, Web of Science, ADS, Google Scholar
24. E. G. Carnio, A. Buchleitner and M. Gessner, Phys. Rev. Lett. 115, 010404 (2015). Crossref, Web of Science, ADS, Google Scholar
25. E. G. Carnio, A. Buchleitner and M. Gessner, New J. Phys. 18, 073010 (2016). Crossref, Web of Science, Google Scholar
26. W. Song, L. Chen and S. L. Zhu, Phys. Rev. A 80, 012331 (2009). Crossref, Web of Science, ADS, Google Scholar
27. M. Ali, Phys. Rev. A 81, 042303 (2010). Crossref, Web of Science, ADS, Google Scholar
28. M. Ghasemi and M. K. Tavassoly, Eur. Phys. J. Plus 131, 297 (2016); E. Faraji, M. K. Tavassoly and H. R. Baghshahi, Int. J. Theor. Phys. 55, 2573 (2016); H. R. Baghshahi and M. K. Tavassoly, Phys. Scripta 89, 075101 (2014); H. R. Baghshahi, M. K. Tavassoly and S. J. Akhtarshenas, Quant. Inform. Proc. 14, 1279 (2015). Google Scholar
29. R. Inoue, T. Yonehara, Y. Miyamoto, M. Koashi and M. Kozuma, Phys. Rev. Lett. 103, 110503 (2009); H. Jaghouri, M. Sarbishaei and K. Javidan, Pramana 86, 997 (2016); X. Xiao and Y.-L. Li, Eur. Phys. J. D 67, 204 (2013). Google Scholar
30. J. S. Bell, Physics 1, 195 (1964). Crossref, Google Scholar
31. N. Gisin, Phys. Lett. A 154, 201 (1991); R. F. Werner, Phys. Rev. A 40, 4277 (1989). Google Scholar
32. Y.-C. Liang, L. Masanes and D. Rosset, Phys. Rev. A 86, 052115 (2011). Crossref, Web of Science, Google Scholar
33. J. F. Clauser, M. A. Horne, A. Shimony and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969). Crossref, Web of Science, ADS, Google Scholar
34. L. Mazzola, B. Bellomo, R. Lo Franco and G. Compagno, Phys. Rev. A 81, 052116 (2010). Crossref, Web of Science, ADS, Google Scholar
35. J.-S. Xu et al., Phys. Rev. Lett. 104, 100502 (2010). Crossref, Web of Science, ADS, Google Scholar
36. W. Laskowski, T. Paterek, C. Brukner and M. Zukowski, Phys. Rev. A 81, 042101 (2010); R. Chaves, D. Cavalcanti, L. Aolita and A. Acin, ibid. 86, 012108 (2012); R. Chaves, A. Acin, L. Aolita and D. Cavalcanti, ibid. 89, 042106 (2014); A. Sohbi, I. Zaquine, E. Diamanti and D. Markham, ibid. 91, 022101 (2015); P. Divianszky, R. Trencsenyi, E. Bene and T. Vertesi, ibid. 93, 042113 (2016); W. Laskowski, T. Vertesi and M. Wiesniak, J. Phys. A: Math. Theor. 48, 465301 (2015). Google Scholar
37. D. Mermin, Phys. Rev Lett. 65, 1838 (1990). Crossref, Web of Science, ADS, Google Scholar
38. M. Ardehali, Phys. Rev. A 46, 5375 (1992). Crossref, Web of Science, ADS, Google Scholar
39. J.-D. Bancal, N. Brunner, N. Gisin and Y.-C. Liang, Phys. Rev. Lett. 106, 020405 (2011). Crossref, Web of Science, ADS, Google Scholar
40. G. Svetlichny, Phys. Rev. D 35, 3066 (1987). Crossref, Web of Science, ADS, Google Scholar
41. D. Collins, N. Gisin, S. Popescu, D. Roberts and V. Scarani, Phys. Rev Lett. 88, 170405 (2002). Crossref, Web of Science, ADS, Google Scholar
42. J.-L. Chen, D. Kaszlikowski, L. C. Kwek, C. H. Oh and M. Zukowski, Phys. Rev. A 64, 052109 (2001). Crossref, Web of Science, ADS, Google Scholar
43. J. W. Pan et al., Nature 403, 515 (2000); J. Lavoie, R. Kaltenbaek and K. J. Resch, New J. Phys. 11, 073051 (2009); C. Erwen et al., Nat. Photonics 8, 292 (2014). Google Scholar
44. B. Jungnitsch et al., Phys. Rev. Lett. 104, 210401 (2010). Crossref, Web of Science, ADS, Google Scholar
45. D. Kaszlikowski, P. Gnaciński, M. Zukowski, W. Miklaszewski and A. Zeilinger, Phys. Rev. Lett. 85, 4418 (2000); T. Durt, D. Kaszlikowski and M. Zukowski, Phys. Rev. A 64, 024101 (2001). Google Scholar
46. D. Kaszlikowski, L. C. Kwek, J.-L. Chen, M. Zukowski and C. H. Oh, Phys. Rev. A 65, 032118 (2002); J.-L. Chen, D. Kaszlikowski, L. C. Kwek and C. H. Oh, Mod. Phys. Lett. A 17, 2231 (2002). Google Scholar
47. J.-L. Chen, C. Wu, L. C. Kwek, C. H. Oh and M.-L. Ge, Phys. Rev. A 74, 032106 (2006). Crossref, Web of Science, ADS, Google Scholar
48. D. Collins, N. Gisin, N. Linden, S. Massar and S. Popescu, Phys. Rev. Lett. 88, 040404 (2002). Crossref, Web of Science, ADS, Google Scholar
49. B. Baumgartner, B. C. Hiesmayr and N. Narnhofer, Phys. Rev. A 74, 032327 (2006); Ł. Derkacz and L. Jakóbczyk, ibid. 76, 042304 (2007). Google Scholar
50. A. Peres, Phys. Rev. Lett. 77, 1413 (1996). Crossref, Web of Science, ADS, Google Scholar
51. L. Clarisse, PhD thesis, University of York, England, arXiv:quant-ph/0612072. Google Scholar
52. K. Chen and L. A. Wu, Quant. Inf. Comput. 3, 193 (2003); O. Rudolph, Quant. Info. Proc. 4, 219 (2005). Google Scholar
53. G. Vidal and R. F. Werner, Phys. Rev. A 65, 032314 (2002). Crossref, Web of Science, ADS, Google Scholar
54. B. Jungnitsch, T. Moroder and O. Gühne, Phys. Rev. Lett. 106, 190502 (2011); L. Novo, T. Moroder and O. Gühne, Phys. Rev. A 88, 012305 (2013); M. Hofmann, T. Moroder and O. Gühne, J. Phys. A: Math. Theor. 47, 155301 (2014). Google Scholar
55. A. Vaziri, G. Weihs and A. Zeilinger, Phys. Rev. Lett. 89, 240401 (2002). Crossref, Web of Science, ADS, Google Scholar
56. D. Alsina, A. Cervera, D. Goyeneche, J. I. Latorre and K. Zyczkowski, Phys. Rev. A 94, 032102 (2016). Crossref, Web of Science, ADS, Google Scholar
57. A. Acin, T. Durt, N. Gisin and J. I. Latorre, Phys. Rev. A 65, 052325 (2002). Crossref, Web of Science, ADS, Google Scholar
58. A. Acin, R. Gill and N. Gisin, Phys. Rev. Lett. 95, 210402 (2005). Crossref, Web of Science, ADS, Google Scholar
59. G. Tóth, Comput. Phys. Commun. 179, 430 (2008). Crossref, Web of Science, ADS, Google Scholar