Skip to main content
Log in

Quantum correlations and decoherence dynamics for a qutrit–qutrit system under random telegraph noise

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

We analyze the effect of a classical random telegraph noise on the dynamics of quantum correlations and decoherence between two non-interacting spin-qutrit particles, initially entangled, and coupled either to independent sources or to a common source of noise. Both Markovian and non-Markovian environments are considered. For the Markov regime, as the noise switching rate decreases, a monotonic decay of the initial quantum correlations is found and the loss of coherence increases monotonically with time up to the saturation value. For the non-Markov regime, evident oscillations of correlations and decoherence are observed due to the noise regime, but correlations, however, avoid sudden death phenomena. The oscillatory behavior is more and more prominent as the noise switching rate decreases in this regime, thus enhancing robustness of correlations. Similarly to the qubits case, independent environments coupling is more effective than a common environment coupling in preserving quantum correlations and coherence of the system for a Markovian noise; meanwhile, the opposite is found for the non-Markovian one.

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

Access this article

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

Instant access to the full article PDF.

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

Similar content being viewed by others

References

  1. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  2. Chekhova, M., Kulik, S., Chekhova, M., Kulik, S.: Physical foundations of quantum electronics. In: Klyshko, D. (eds.) 1st ed., WS (2011)

  3. Grassani, D., Azzini, S., Liscidini, M., Galli, M., Strain, M.J., Sorel, M., Sipe, J.E., Bajoni, D.: Micrometer-scale integrated silicon source of time-energy entangled photons. Optica 2(2), 88–94 (2015)

    Article  Google Scholar 

  4. Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70(13), 1895–1899 (1993)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Boschi, D., Branca, S., De Martini, F., Hardy, L., Popescu, S.: Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 80(6), 1121–1125 (1998)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Bennett, C.H., Wiesner, S.J.: Communication via one- and two-particle operators on Einstein–Podolsky–Rosen states. Phys. Rev. Lett. 69(20), 2881–2884 (1992)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Mattle, K., Weinfurter, H., Kwiat, P.G., Zeilinger, A.: Dense coding in experimental quantum communication. Phys. Rev. Lett. 76(25), 4656–4659 (1996)

    Article  ADS  Google Scholar 

  8. Deutsch, D., Jozsa, R.: Rapid solution of problems by quantum computation. Proc. R. Soc. Math. Phys. Eng. Sci. 439(1907), 553–558 (1992)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. Ekert, A., Jozsa, R.: Quantum computation and Shors factoring algorithm. Rev. Mod. Phys. 68(3), 733–753 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  10. Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79(2), 325–328 (1997)

    Article  ADS  Google Scholar 

  11. Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74(1), 145–195 (2002)

    Article  ADS  Google Scholar 

  12. Long, G.L., Liu, X.S.: Theoretically efficient high-capacity quantum-key-distribution scheme. Phys. Rev. A 65(3), 032302 (2002)

    Article  ADS  Google Scholar 

  13. Boström, K., Felbinger, T.: Deterministic secure direct communication using entanglement. Phys. Rev. Lett. 89(18), 187902 (2002)

    Article  ADS  Google Scholar 

  14. Joos, E., Zeh, H.D., Kiefer, C., Giulini, D., Kupsch, J., Stamatescu, I.-O.: Decoherence and the Appearance of a Classical World in Quantum Theory. Springer, Berlin (2003)

    Book  MATH  Google Scholar 

  15. Zurek, W.H.: Decoherence, einselection, and the quantum origins of the classical. Rev. Mod. Phys. 75(3), 715775 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  16. Yu, T., Eberly, J.H.: Finite-time disentanglement via spontaneous emission. Phys. Rev. Lett. 93(14), 140404 (2004)

    Article  ADS  Google Scholar 

  17. Bellomo, B., Lo Franco, R., Maniscalco, S., Compagno, G.: Entanglement trapping in structured environments. Phys. Rev. A 78(6), 060302(R) (2008)

    Article  ADS  Google Scholar 

  18. Maniscalco, S., Francica, F., Zaffino, R. L., Lo Gullo, N., Plastina, F.: Protecting entanglement via the quantum zeno effect. Phys. Rev. Lett. 100(9), 090503 (2008)

  19. Buscemi, F., Bordone, P., Bertoni, A.: Validity of the single-particle approach for electron transport in quantum wires assisted by surface acoustic waves. J. Phys. Condens. Matter 21(30), 305303 (2009)

    Article  Google Scholar 

  20. Yu, T., Eberly, J.H.: Sudden death of entanglement. Science 323(5914), 598601 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  21. Yu, T., Eberly, J. H.: Quantum open system theory: bipartite aspects. Phys. Rev. Lett. 97(14), 140403 (2006)

  22. Bellomo, B., Lo Franco, R., Compagno, G.: Non-Markovian effects on the dynamics of entanglement. Phys. Rev. Lett. 99(16), 160502 (2007)

    Article  ADS  Google Scholar 

  23. Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80(10), 2245–2248 (1998)

    Article  ADS  Google Scholar 

  24. Coffman, V., Kundu, J., Wootters, W.K.: Distributed entanglement. Phys. Rev. A 61(5), 052306 (2000)

    Article  ADS  Google Scholar 

  25. Vidal, G.: Entanglement monotones. J. Mod. Opt. 47(2–3), 355–376 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  26. Vidal, G., Werner, R.F.: Computable measure of entanglement. Phys. Rev. A 65(3), 032314 (2002)

    Article  ADS  Google Scholar 

  27. Gühne, O., Tóth, G.: Entanglement detection. Phys. Rep. 474(1–6), 1–75 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  28. Datta, A., Shaji, A., Caves, C.M.: Quantum discord and the power of one qubit. Phys. Rev. Lett. 100(5), 050502 (2008)

    Article  ADS  Google Scholar 

  29. Lanyon, B.P., Barbieri, M., Almeida, M.P., White, A.G.: Experimental quantum computing without entanglement. Phys. Rev. Lett. 101(20), 200501 (2008)

    Article  ADS  Google Scholar 

  30. Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88(1), 017901 (2001)

    Article  ADS  MATH  Google Scholar 

  31. Henderson, L., Vedral, V.: Classical, quantum and total correlations. J. Phys. Math. Gen. 34(35), 6899–6905 (2001)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  32. Luo, S.: Quantum discord for two-qubit systems. Phys. Rev. A 77(4), 042303 (2008)

  33. Girolami, D., Adesso, G.: Quantum discord for general two-qubit states: analytical progress. Phys. Rev. A 83(5), 052108 (2011)

  34. Ciccarello, F., Giovannetti, V.: Creating quantum correlations through local nonunitary memoryless channels. Phys. Rev. A 85(1), 010102 (2012)

    Article  ADS  Google Scholar 

  35. Werlang, T., Rigolin, G.: Thermal and magnetic quantum discord in Heisenberg models. Phys. Rev. A 81(4), 044101 (2010)

    Article  ADS  Google Scholar 

  36. Kuznetsova, E.I., Zenchuk, A.I.: Quantum discord versus second-order MQ NMR coherence intensity in dimers. Phys. Lett. A 376(10–11), 1029–1034 (2012)

    Article  ADS  MATH  Google Scholar 

  37. Sarandy, M. S.: Classical correlation and quantum discord in critical systems. Phys. Rev. A 80(2), 022108 (2009)

  38. Luo, S.: Using measurement-induced disturbance to characterize correlations as classical or quantum. Phys. Rev. A 77(2), 022301 (2008)

    Article  ADS  Google Scholar 

  39. Benedetti, C., Buscemi, F., Bordone, P., Paris, M.G.A.: Effects of classical environmental noise on entanglement and quantum discord dynamics. Int. J. Quantum Inf. 10(08), 1241005 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  40. Benedetti, C., Buscemi, F., Bordone, P., Paris, M.G.A.: Dynamics of quantum correlations in colored-noise environments. Phys. Rev. A 87(5), 052328 (2013)

    Article  ADS  Google Scholar 

  41. Javed, M., Khan, S., Ullah, S.A.: The dynamics of quantum correlations in mixed classical environments. J. Russ. Laser Res. 37(6), 562571 (2016)

    Article  Google Scholar 

  42. Jia, L.-X., Li, B., Yue, R.-H., Fan, H.: Sudden change of quantum discord under single qubit noise. Int. J. Quantum Inf. 11(05), 1350048 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  43. Kaszlikowski, D., Gnaciski, P., Żukowski, M., Miklaszewski, W., Zeilinger, A.: Violations of local realism by two entangled N-dimensional systems are stronger than for two qubits. Phys. Rev. Lett. 85(21), 44184421 (2000)

    Article  Google Scholar 

  44. Chen, J.-L., Kaszlikowski, D., Kwek, L.C., Oh, C.H., Ukowski, M.: Entangled three-state systems violate local realism more strongly than qubits: an analytical proof. Phys. Rev. A 64(5), 052109 (2001)

    Article  ADS  Google Scholar 

  45. Son, W., Lee, J., Kim, M.S.: Generic bell inequalities for multipartite arbitrary dimensional systems. Phys. Rev. Lett. 96(6), 060406 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  46. Collins, D., Gisin, N., Linden, N., Massar, S., Popescu, S.: Bell inequalities for arbitrarily high-dimensional systems. Phys. Rev. Lett. 88(4), 040404 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  47. Walborn, S.P., Lemelle, D.S., Almeida, M.P., Ribeiro, P.H.S.: Quantum key distribution with higher-order alphabets using spatially encoded qudits. Phys. Rev. Lett. 96(9), 090501 (2006)

    Article  ADS  Google Scholar 

  48. Wang, S., Lu, Y., Long, G.-L.: Entanglement classification of \(222d\) quantum systems via the ranks of the multiple coefficient matrices. Phys. Rev. A 87(6), 062305 (2013)

    Article  ADS  Google Scholar 

  49. Bourennane, M., Karlsson, A., Björk, G.: Quantum key distribution using multilevel encoding. Phys. Rev. A 64(1), 012306 (2001)

    Article  ADS  Google Scholar 

  50. Da-Sheng, D., Cheng-Jie, Z., Yong-Sheng, Z., Guang-Can, G. U. O., Da-Sheng, D., Cheng-Jie, Z., Yong-Sheng, Z., Guang-Can, G. U. O.: Class of unlockable bound entangled states and their applications. Chin. Phys. Lett. 25(7), 2366–2369 (2008)

  51. Horodecki, P., Horodecki, M., Horodecki, R.: Bound entanglement can be activated. Phys. Rev. Lett. 82(5), 1056–1059 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  52. Ali, M.: Distillability sudden death in qutrit–qutrit systems under global and multilocal dephasing. Phys. Rev. A 81(4), 042303 (2010)

    Article  ADS  Google Scholar 

  53. Klyachko, A.A., Öztop, B., Shumovsky, A.S.: Entanglement of qutrits. Laser Phys. 17(2), 226229 (2007)

    Google Scholar 

  54. Zhen-Biao, Y., Huai-Zhi, W., Shi-Biao, Z.: Robust generation of qutrit entanglement via adiabatic passage of dark states. Chin. Phys. B 19(9), 094205 (2010)

    Article  ADS  Google Scholar 

  55. Cerf, N.J., Bourennane, M., Karlsson, A., Gisin, N.: Security of quantum key distribution using \(\mathit{d}\)-level systems. Phys. Rev. Lett. 88(12), 127902 (2002)

    Article  ADS  Google Scholar 

  56. Durt, T., Cerf, N.J., Gisin, N., Zukowski, M.: Security of quantum key distribution with entangled qutrits. Phys. Rev. A 67(1), 012311 (2003)

    Article  ADS  Google Scholar 

  57. Vallone, G., Pomarico, E., De Martini, F., Mataloni, P., Barbieri, M.: Experimental realization of polarization qutrits from nonmaximally entangled states. Phys. Rev. A 76(1), 012319 (2007)

    Article  ADS  Google Scholar 

  58. Jafarpour, M.: An entanglement study of superposition of qutrit spin-coherent states. J. Sci. Islam. Repub. Iran 22(2), 165169 (2011)

    Google Scholar 

  59. Bose, S.: Quantum communication through an unmodulated spin chain. Phys. Rev. Lett. 91(20), 207901 (2003)

    Article  ADS  Google Scholar 

  60. Ivanchenko, E. A.: Qutrit: entanglement dynamics in the finite qutrit chain in the consistent magnetic field. arXiv:1106.2297 [quant-ph] (2011)

  61. Jafarpour, M., Ashrafpour, M.: Entanglement dynamics of a two-qutrit system under DM interaction and the relevance of the initial state. Quantum Inf. Process. 12(2), 761–772 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  62. Doustimotlagh, N., Guo, J.-L., Wang, S.: Quantum correlations in qutrit–qutrit systems under local quantum noise channels. Int. J. Theor. Phys. 54(6), 1784–1797 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  63. Yang, Y., Wang, A.-M.: Quantum discord for a qutrit–qutrit system under depolarizing and dephasing noise. Chin. Phys. Lett. 30(8), 080302 (2013)

    Article  ADS  Google Scholar 

  64. Li, X.-J., Ji, H.-H., Hou, X.-W.: Thermal discord and negativity in a two-spin-qutrit system under different magnetic fields. Int. J. Quantum Inf. 11(08), 1350070 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  65. Jafarpour, M., Naderi, N.: Qutrit teleportation under intrinsic decoherence. Int. J. Quantum Inf. 14(05), 1650028 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  66. Jaeger, G., Ann, K.: Disentanglement and decoherence in a pair of qutrits under dephasing noise. J. Mod. Opt. 54(16–17), 2327–2338 (2007)

    Article  ADS  Google Scholar 

  67. Ali, M.: Distillability sudden death in qutrit-qutrit systems under amplitude damping. J. Phys. B At. Mol. Opt. Phys. 43(4), 045504 (2010)

    Article  ADS  Google Scholar 

  68. Gruca, J., Laskowski, W., Żukowski, M.: Nonclassicality of pure two-qutrit entangled states. Phys. Rev. A 85(2), 022118 (2012)

    Article  ADS  Google Scholar 

  69. Fujisawa, T., Hirayama, Y.: Charge noise analysis of an AlGaAs/GaAs quantum dot using transmission-type radio-frequency single-electron transistor technique. Appl. Phys. Lett. 77(4), 543–545 (2000)

    Article  ADS  Google Scholar 

  70. Falci, G., DArrigo, A., Mastellone, A., Paladino, E.: Initial decoherence in solid state qubits. Phys. Rev. Lett. 94(16), 167002 (2005)

    Article  ADS  Google Scholar 

  71. Paladino, E., Faoro, L., Falci, G., Fazio, R.: Decoherence and \(1/\mathit{f}\) Noise in Josephson qubits. Phys. Rev. Lett. 88(22), 228304 (2002)

    Article  ADS  Google Scholar 

  72. Jakóbczyk, L., Frydryszak, A., Lugiewicz, P.: Qutrit geometric discord. Phys. Lett. A 380(17), 1535–1541 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  73. Ali, M., Rau, A.R.P., Alber, G.: Quantum discord for two-qubit X states. Phys. Rev. A 81(4), 042105 (2010)

    Article  ADS  Google Scholar 

  74. Beggi, A., Buscemi, F., Bordone, P.: Analytical expression of genuine tripartite quantum discord for symmetrical X-states. Quantum Inf. Process. 14(2), 573–592 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Arthur Tsamouo Tsokeng.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tsokeng, A.T., Tchoffo, M. & Fai, L.C. Quantum correlations and decoherence dynamics for a qutrit–qutrit system under random telegraph noise. Quantum Inf Process 16, 191 (2017). https://doi.org/10.1007/s11128-017-1645-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-017-1645-4

Keywords

Navigation