Skip to main content
SpringerLink
Log in

Qubit-Qutrit (2 ⊗ 3) Quantum Systems: an Investigation of Some Quantum Correlations Under Collective Dephasing

  • General and Applied Physics
  • Published:
Brazilian Journal of Physics Aims and scope Submit manuscript

Abstract

We revisit qubit-qutrit quantum systems under collective dephasing and answer some of the questions which have not been asked and addressed so far in the literature. In particular, we examine the possibilities of non-trivial phenomena of time-invariant entanglement and freezing dynamics of entanglement for this dimension of Hilbert space. Interestingly, we find that for qubit-qutrit systems both of these peculiar features coexist, that is, we observe not only time-invariant entanglement for certain quantum states but we also find evidence that many quantum states freeze their entanglement after decaying for some time. To our knowledge, the existence of both these phenomena for a dimension of Hilbert space is not found so far. All previous studies suggest that if there is freezing dynamics of entanglement, then there is no time-invariant entanglement and vice versa. In addition, we study local quantum uncertainty and other correlations for certain families of states and discuss the interesting dynamics. Our study is an extension of similar studies for qubit-qubit, qubit-qutrit, and multipartite quantum systems.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. B. Dakic, et al., . Nat. Phys. 8, 666 (2012)

    Google Scholar 

  2. A. Streltsov, H. Kempermann, D. Bruß, . Phys. Rev. Lett. 108, 250501 (2012)

    ADS  Google Scholar 

  3. T.K. Chuan, et al., . Phys. Rev. Lett. 109, 070501 (2012)

    ADS  Google Scholar 

  4. A. Streltsov, W.H. Zurek, . Phys. Rev. Lett. 111, 040401 (2013)

    ADS  Google Scholar 

  5. K. Modi, H. Cable, M. Williamson, V. Vdral, . Phys. Rev. X. 1, 021022 (2011)

    Google Scholar 

  6. R. Horodecki, et al., . Rev. Mod. Phys. 81, 865 (2009)

    ADS  Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

  8. G.D. Chiara, A. Sanpera, . Rep. Prog. Phys. 81, 074002 (2018)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  10. W. Dür, H.J. Briegel, . Phys. Rev. Lett. 92, 180403 (2004)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  12. L. Aolita, et al., . Phys. Rev. Lett. 100, 080501 (2008)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  14. A. Borras, et al., . Phys. Rev. A. 79, 022108 (2009)

    ADS  Google Scholar 

  15. D. Cavalcanti, et al., . Phys. Rev. Lett. 103, 030502 (2009)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  18. L. Aolita, et al., . Phys. Rev. A. 82, 032317 (2010)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  23. A.R.P. Rau, M. Ali, G. Alber, . EPL. 82, 40002 (2008)

    ADS  Google Scholar 

  24. M. Ali, G. Alber, A.R.P. Rau, . J. Phys. B: At. Mol. Opt. Phys. 42, 025501 (2009)

    ADS  Google Scholar 

  25. M. Ali, . J. Phys. B: At. Mol. Opt. Phys. 43, 045504 (2010)

    ADS  Google Scholar 

  26. Y.S. Weinstein, et al., . Phys. Rev. A. 85, 032324 (2012)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  28. M. Ali, O. Gühne, . J. Phys. B: At. Mol. Opt. Phys. 47, 055503 (2014)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  31. M. Ali, . Open. Sys. & Info. Dyn. 21(4), 1450008 (2014)

    Google Scholar 

  32. M. Ali, . Chin. Phys. B. 24(12), 120303 (2015)

    Google Scholar 

  33. M. Ali, . Chin. Phys. Lett. 32(6), 060302 (2015)

    ADS  Google Scholar 

  34. M. Ali, . Int. J. Quant. Info. 14(7), 1650039 (2016)

    Google Scholar 

  35. W.H. Zurek, . Rev. Mod. Phys. 75, 715 (2003)

    ADS  Google Scholar 

  36. http://www.theory.caltech.edu/people/preskill/ph229/

  37. H.P. Breuer, F. Petruccione. The Theory of Open Systems (Oxford University Press, New York, 2002), p. 3

    MATH  Google Scholar 

  38. B. de Lima Bernardo, . Braz. J. Phys. 44, 202 (2014)

    ADS  Google Scholar 

  39. A.-B. A. Mohamed, N. Metwally, . Ann. Phys. 381, 137 (2017)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  43. G. Jaeger, K. Ann, . J. Mod. Opt. 54(16), 2327 (2007)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  45. W. Song, L. Chen, S.L. Zhu, . Phys. Rev. A. 80, 012331 (2009)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  48. M.O. Scully, M.S. Zubairy, Quanum Optics. Cambridge University Press. ch 8 (1997)

  49. H.-H. Liu, et al., . Phys. Rev. A. 94, 062107 (2016)

    ADS  Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

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

    Google Scholar 

  52. M. Ali, . Int. J. Quant. Info. 15(3), 1750022 (2017)

    Google Scholar 

  53. M. Ali, . Eur. Phys. J. D. 71, 1 (2017)

    ADS  Google Scholar 

  54. M. Ali, . Mod. Phys. Lett. A. 33(1), 1950102 (2019)

    Google Scholar 

  55. H. Ollivier, W.H. Zurek, . Phys. Rev. Lett. 88, 017901 (2001)

    ADS  Google Scholar 

  56. L. Henderson, V. Vedral, . J. Phys. A. 34, 6899 (2001)

    ADS  MathSciNet  Google Scholar 

  57. V. Vedral, . Phys. Rev. Lett. 90, 050401 (2003)

    ADS  Google Scholar 

  58. J. Maziero, L.C. Celéri, R.M. Serra, V. Vedral, . Phys. Rev A. 80, 044102 (2009)

    ADS  MathSciNet  Google Scholar 

  59. S. Luo, . Phys. Rev. A. 77, 042303 (2008)

    ADS  Google Scholar 

  60. M. Ali, A.R.P. Rau, G. Alber, . Phys. Rev A. 81, 042105 (2010)

    ADS  Google Scholar 

  61. M. Ali, . J. Phys. A: Math. Theor. 43, 495303 (2010)

    ADS  Google Scholar 

  62. S. Vinjanampathy, A.R.P. Rau, . J. Phys. A: Math. Theor. 45, 095303 (2012)

    ADS  Google Scholar 

  63. A.R.P. Rau, . Quant. Info. Proc. 17, 216 (2018)

    Google Scholar 

  64. T. Werlang, S. Souza, F.F. Fanchini, C.J. Villas-Boas, . Phys. Rev A. 80, 024103 (2009)

    ADS  Google Scholar 

  65. J. Maziero, T. Werlang, F.F. Fanchini, L.C. Celeri, R.M. Serra, . Phys. Rev A. 81, 022116 (2010)

    ADS  Google Scholar 

  66. F.F. Fanchini, T. Werlang, C.A. Brasil, L.G.E. Arruda, A.O. Caldeira, . Phys. Rev A. 81, 052107 (2010)

    ADS  Google Scholar 

  67. D. Girolami, T. Tufarelli, G. Adesso, . Phys. Rev. Lett. 110, 240402 (2013)

    ADS  Google Scholar 

  68. K. Modi, A. Brodutch, H. Cable, T. Paterek, V. Vedral, . Rev. Mod. Phys. 84, 1655 (2012)

    ADS  Google Scholar 

  69. A. Bera, T. Das, D. Sadhukhan, S.S. Roy, A. Sen De, U. Sen, . Rep. Prog. Phys. 81, 024001 (2018)

    ADS  Google Scholar 

  70. G. Karpat, . Can. J. Phys. 96(7), 705 (2018)

    ADS  Google Scholar 

  71. A. Slaoui, M.I. Shaukat, M. Daoud, R. Ahl Laamara, . Eur. Phys. J. Plus. 133, 413 (2018)

    Google Scholar 

  72. A. Slaoui, M. Daoud, R. Ahl Laamara, . Quan. Info. Proc. 17(7), 178 (2018)

    Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

  74. C.H. Bennett, D.P. DiVincenzo, J. Wootters, W.K. Smolin, . Phys. Rev. A. 54, 3824 (1996)

    ADS  MathSciNet  Google Scholar 

  75. S. Hill, W.K. Wootters, . Phys. Rev. Lett. 78, 5022 (1997)

    ADS  Google Scholar 

  76. W.K. Wootters, . Phys. Rev. Lett. 80, 2245 (1998)

    ADS  Google Scholar 

  77. A. Sanpera, D. Bruß, M. Lewenstein, . Phys. Rev. A. 63, 050301 (2001)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  82. B. Groisman, S. Popescu, A. Winter, . Phys. Rev. A. 72, 032317 (2005)

    ADS  MathSciNet  Google Scholar 

  83. D.P. Chi, S. Lee, . J. Phys. A: Math. Theor. 36, 11503 (2003)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  85. G. Tóth, . Comput. Phys. Comm. 179, 430 (2008)

    ADS  MathSciNet  Google Scholar 

Download references

Acknowledgments

The author is grateful to the referee for his/her positive comments which brought more clarity in the manuscript.

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.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ali, M. Qubit-Qutrit (2 ⊗ 3) Quantum Systems: an Investigation of Some Quantum Correlations Under Collective Dephasing. Braz J Phys 50, 124–135 (2020). https://doi.org/10.1007/s13538-019-00721-1

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13538-019-00721-1

Keywords

Search

Navigation