Disentanglement and quantum states transitions dynamics in spin-qutrit systems: dephasing random telegraph noise and the relevance of the initial state

  • Tsamouo Tsokeng Arthur
  • Tchoffo Martin
  • Lukong Cornelius Fai
Article
  • 200 Downloads

Abstract

Using negativity and realignment criterion as quantifiers of free and bound entanglements respectively, we present in details the analytical study of the entanglements and quantum states transitions dynamics in a two-qutrit system driven by dephasing random telegraph noise channel(s). Both collective and independent system–environment couplings as well as the Markovian and the non-Markovian regimes of the noise channel(s) are considered. Two non-equivalent initial states and their locally equivalent through a local unitary operation (LUO) are also considered. We demonstrate a stronger entanglement under independent Markovian environments than with a collective one; meanwhile, for the non-Markovian regime, entanglement is stronger under a collective environment than with independent ones. States transitions as well as the (re)activation of bound entanglement (for initially free entangled states) can be found for a specific class of initial states, but can, however, be avoided by means of a LUO on the initial state. While unavoidable disentanglement occurs for independents coupling, we demonstrate the possibility of indefinite free entanglement survival in the qutrit system under a common environment by converting the initial entangled state using the local unitary operation.

Keywords

Qutrit Entanglement State transitions Dephasing Random telegraph noise 

References

  1. 1.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)MATHGoogle Scholar
  2. 2.
    Cui, J., Gu, M., Kwek, L.C., Santos, M.F., Fan, H., Vedral, V.: Quantum phases with differing computational power. Nat. Commun. 3, 812 (2012)CrossRefADSGoogle Scholar
  3. 3.
    Ekert, A.K.: Quantum cryptography based on Bells theorem. Phys. Rev. Lett. 67(6), 661 (1991)MathSciNetCrossRefMATHADSGoogle Scholar
  4. 4.
    Bennett, C.H., Brassard, G., Crpeau, 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 (1993)MathSciNetCrossRefMATHADSGoogle Scholar
  5. 5.
    Murao, M., Jonathan, D., Plenio, M.B., Vedral, V.: Quantum telecloning and multiparticle entanglement. Phys. Rev. A 59(1), 156 (1999)CrossRefADSGoogle Scholar
  6. 6.
    Raussendorf, R., Briegel, H.J.: A one-way quantum computer. Phys. Rev. Lett. 86(22), 5188 (2001)CrossRefADSGoogle Scholar
  7. 7.
    Richter, T., Vogel, W.: Nonclassical characteristic functions for highly sensitive measurements. Phys. Rev. A 76(5), 053835 (2007)CrossRefADSGoogle Scholar
  8. 8.
    Hu, C.Y., Rarity, J.G.: Loss-resistant state teleportation and entanglement swapping using a quantum-dot spin in an optical microcavity. Phys. Rev. B 83(11), 115303 (2011)CrossRefADSGoogle Scholar
  9. 9.
    Chekhova, M., Kulik, S., Chekhova, M., Kulik, S.: Physical Foundations of Quantum Electronics by David Klyshko, 1st edn. WS, Singpore (2011)CrossRefGoogle Scholar
  10. 10.
    Moreva, E., Brida, G., Gramegna, M., Giovannetti, V., Maccone, L., Genovese, M.: Time from quantum entanglement: an experimental illustration. Phys. Rev. A 89(5), 052122 (2014)CrossRefADSGoogle Scholar
  11. 11.
    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 (2015)CrossRefGoogle Scholar
  12. 12.
    Zurek, W.H.: Decoherence, einselection, and the quantum origins of the classical. Rev. Mod. Phys. 75(3), 715 (2003)MathSciNetCrossRefMATHADSGoogle Scholar
  13. 13.
    Yu, T., Eberly, J.H.: Finite-time disentanglement via spontaneous emission. Phys. Rev. Lett. 93(14), 140404 (2004)CrossRefADSGoogle Scholar
  14. 14.
    Yu, T., Eberly, J.: Sudden death of entanglement: classical noise effects. Opt. Commun. 264(2), 393 (2006)CrossRefADSGoogle Scholar
  15. 15.
    Yu, T., Eberly, J.H.: Sudden death of entanglement. Science 323(5914), 598 (2009)MathSciNetCrossRefMATHADSGoogle Scholar
  16. 16.
    Lopez, C.E., Romero, G., Lastra, F., Solano, E., Retamal, J.C.: Sudden birth versus sudden death of entanglement in multipartite systems. Phys. Rev. Lett. 101(8), 080503 (2008)CrossRefADSGoogle Scholar
  17. 17.
    Lo Franco, R., Bellomo, B., Andersson, E., Compagno, G.: Revival of quantum correlations without system environment back-action. Phys. Rev. A 85(3), 032318 (2012)CrossRefADSGoogle Scholar
  18. 18.
    Xu, J.S., Sun, K., Li, C.F., Xu, X.Y., Guo, G.C., Andersson, E., Franco, R.L., Compagno, G.: Experimental recovery of quantum correlations in absence of system environment back-action. Nat. Commun. 4, 2851 (2013)Google Scholar
  19. 19.
    Bellomo, B., Lo Franco, R., Compagno, G.: Entanglement dynamics of two independent qubits in environments with and without memory. Phys. Rev. A 77(3), 032342 (2008)CrossRefADSGoogle Scholar
  20. 20.
    Mazzola, L.: Sudden death and sudden birth of entanglement in common structured reservoirs. Phys. Rev. A 79(4), 042302 (2009)CrossRefADSGoogle Scholar
  21. 21.
    Hu, J.: Entanglement dynamics for uniformly accelerated two-level atoms. Phys. Rev. A 91(1), 012327 (2015)MathSciNetCrossRefADSGoogle Scholar
  22. 22.
    Huang, Z., Qiu, D., Mateus, P.: Geometry and dynamics of one-norm geometric quantum discord. Quantum Inf. Process. 15(1), 301 (2016)MathSciNetCrossRefMATHADSGoogle Scholar
  23. 23.
    Situ, H., Hu, X.: Dynamics of relative entropy of coherence under Markovian channels. Quantum Inf. Process. 15(11), 4649 (2016)MathSciNetCrossRefMATHADSGoogle Scholar
  24. 24.
    Huang, Z., Situ, H.: Non-Markovian dynamics of quantum coherence of two-level system driven by classical field. Quantum Inf. Process. 16(9), 222 (2017)MathSciNetCrossRefADSGoogle Scholar
  25. 25.
    Huang, Z., Tian, Z.: Dynamics of quantum entanglement in de Sitter spacetime and thermal Minkowski spacetime. Nucl. Phys. B 923, 458 (2017)MathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    Bellomo, B., Lo Franco, R., Compagno, G.: Non-Markovian effects on the dynamics of entanglement. Phys. Rev. Lett. 99(16), 160502 (2007)CrossRefADSGoogle Scholar
  27. 27.
    Girolami, D., Adesso, G.: Quantum discord for general two-qubit states: analytical progress. Phys. Rev. A 83(5), 052108 (2011)CrossRefADSGoogle Scholar
  28. 28.
    Ciccarello, F., Giovannetti, V.: Creating quantum correlations through local nonunitary memoryless channels. Phys. Rev. A 85(1), 010102 (2012)CrossRefADSGoogle Scholar
  29. 29.
    Kuznetsova, E., Zenchuk, A.: Quantum discord versus second-order MQ NMR coherence intensity in dimers. Phys. Lett. A 376(10–11), 1029 (2012)CrossRefMATHADSGoogle Scholar
  30. 30.
    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)CrossRefADSGoogle Scholar
  31. 31.
    Javed, M., Khan, S., Ullah, S.A.: The dynamics of quantum correlations in mixed classical environments. J. Russ. Laser Res. 37(6), 562 (2016)CrossRefGoogle Scholar
  32. 32.
    Kaszlikowski, D., Gnaciski, P., ukowski, 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), 4418 (2000)CrossRefADSGoogle Scholar
  33. 33.
    Collins, D., Gisin, N., Linden, N., Massar, S., Popescu, S.: Bell inequalities for arbitrarily high-dimensional systems. Phys. Rev. Lett. 88(4), 040404 (2002)MathSciNetCrossRefMATHADSGoogle Scholar
  34. 34.
    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)CrossRefADSGoogle Scholar
  35. 35.
    Bourennane, M., Karlsson, A., Bjrk, G.: Quantum key distribution using multilevel encoding. Phys. Rev. A 64(1), 012306 (2001)CrossRefADSGoogle Scholar
  36. 36.
    Da-Sheng, D., Cheng-Jie, Z., Yong-Sheng, Z., Guang-Can, G.U.O.: Class of unlockable bound entangled states and their applications, class of unlockable bound entangled states and their applications. Chin. Phys. Lett. 25(7), 2366 (2008)CrossRefADSGoogle Scholar
  37. 37.
    Horodecki, P., Horodecki, M., Horodecki, R.: Bound entanglement can be activated. Phys. Rev. Lett. 82(5), 1056 (1999)MathSciNetCrossRefMATHADSGoogle Scholar
  38. 38.
    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)CrossRefGoogle Scholar
  39. 39.
    Durt, T., Cerf, N.J., Gisin, N., Żukowski, M.: Security of quantum key distribution with entangled qutrits. Phys. Rev. A 67(1), 012311 (2003)CrossRefADSGoogle Scholar
  40. 40.
    Jafarpour, M.: An entanglement study of superposition of qutrit spin-coherent states. J. Sci. Islam. Repub. Iran 22(2), 165 (2011)Google Scholar
  41. 41.
    Ali, M.: Distillability sudden death in qutrit\(-\)qutrit systems under global and multilocal dephasing. Phys. Rev. A 81(4), 042303 (2010)CrossRefGoogle Scholar
  42. 42.
    Ali, M.: Distillability sudden death in qutrit-qutrit systems under amplitude damping. J. Phys. B: At. Mol. Opt. Phys. 43(4), 045504 (2010)CrossRefADSGoogle Scholar
  43. 43.
    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 (2013)MathSciNetCrossRefMATHADSGoogle Scholar
  44. 44.
    Yang, Y., Wang, A.M.: Quantum discord for a qutrit\(-\)qutrit system under depolarizing and dephasing noise. Chin. Phys. Lett. 30(8), 080302 (2013)CrossRefGoogle Scholar
  45. 45.
    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)MathSciNetCrossRefMATHADSGoogle Scholar
  46. 46.
    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 (2015)MathSciNetCrossRefMATHGoogle Scholar
  47. 47.
    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(8), 191 (2017)MathSciNetCrossRefMATHADSGoogle Scholar
  48. 48.
    Arthur, T.T., Martin, T., Fai, L.C.: Quantum correlations and coherence dynamics in qutrit–qutrit systems under mixed classical environmental noises. Int. J. Quantum Inform. 15(06), 1750047 (2017)MathSciNetCrossRefMATHADSGoogle Scholar
  49. 49.
    Horodecki, M., Horodecki, P., Horodecki, R.: Mixed-state entanglement and distillation: is there a bound entanglement in nature? Phys. Rev. Lett. 80(24), 5239 (1998)MathSciNetCrossRefMATHADSGoogle Scholar
  50. 50.
    Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81(2), 865 (2009)MathSciNetCrossRefMATHADSGoogle Scholar
  51. 51.
    Smolin, J.A.: Four-party unlockable bound entangled state. Phys. Rev. A 63(3), 032306 (2001)CrossRefADSGoogle Scholar
  52. 52.
    Acin, A., Cirac, J.I., Masanes, L.: Multipartite bound information exists and can be activated. Phys. Rev. Lett. 92(10), 107903 (2004)CrossRefADSGoogle Scholar
  53. 53.
    Shor, P.W., Smolin, J.A., Thapliyal, A.V.: Superactivation of bound entanglement. Phys. Rev. Lett. 90(10), 107901 (2003)MathSciNetCrossRefMATHADSGoogle Scholar
  54. 54.
    Horodecki, K., Horodecki, M., Horodecki, P., Oppenheim, J.: Secure key from bound entanglement. Phys. Rev. Lett. 94(16), 160502 (2005)MathSciNetCrossRefMATHADSGoogle Scholar
  55. 55.
    Murao, M., Vedral, V.: Remote information concentration using a bound entangled state. Phys. Rev. Lett. 86(2), 352 (2001)CrossRefADSGoogle Scholar
  56. 56.
    Ishizaka, S.: Bound entanglement provides convertibility of pure entangled states. Phys. Rev. Lett. 93(19), 190501 (2004)CrossRefADSGoogle Scholar
  57. 57.
    Song, W., Chen, L., Zhu, S.L.: Sudden death of distillability in qutrit-qutrit systems. Phys. Rev. A 80(1), 012331 (2009)CrossRefADSGoogle Scholar
  58. 58.
    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 (2000)CrossRefADSGoogle Scholar
  59. 59.
    Paladino, E., Faoro, L., Falci, G., Fazio, R.: Decoherence and \(1/\mathit{f}\) noise in Josephson qubits. Phys. Rev. Lett. 88(22), 228304 (2002)CrossRefGoogle Scholar
  60. 60.
    Rau, A.R.P., Ali, M., Alber, G.: Hastening, delaying, or averting sudden death of quantum entanglement. EPL 82(4), 40002 (2008)CrossRefADSGoogle Scholar
  61. 61.
    Ali, M., Alber, G., Rau, A.R.P.: Manipulating entanglement sudden death of two-qubit X-states in zero- and finite-temperature reservoirs. J. Phys. B: At. Mol. Opt. Phys. 42(2), 025501 (2009)CrossRefADSGoogle Scholar
  62. 62.
    Vidal, G., Werner, R.F.: Computable measure of entanglement. Phys. Rev. A 65(3), 032314 (2002)CrossRefADSGoogle Scholar
  63. 63.
    Chen, K., Wu, L.A.: A matrix realignment method for recognizing entanglement. arXiv:quant-ph/0205017 (2002)
  64. 64.
    Rudolph, O.: Further results on the cross norm criterion for separability. Quantum Inf. Process. 4(3), 219 (2005)MathSciNetCrossRefMATHGoogle Scholar
  65. 65.
    Clarisse, L.: Entanglement distillation; a discourse on bound entanglement in quantum information theory. arXiv:quant-ph/0612072 (2006)
  66. 66.
    Vaziri, A., Weihs, G., Zeilinger, A.: Experimental twophoton, three-dimensional entanglement for quantum communication. Phys. Rev. Lett. 89(24), 240401 (2002)CrossRefADSGoogle Scholar
  67. 67.
    Thew, R.T., Acin, A., Zbinden, H., Gisin, N.: Experimental realization of entangled qutrits for quantum communication. arXiv:quant-ph/0307122 (2003)
  68. 68.
    Gutierrez-Esparza, A.J., Pimenta, W.M., Marques, B., Matoso, A.A., Pdua, S.: Experimental characterization of two spatial qutrits using entanglement witnesses. Opt. Express 20(24), 26351 (2012)CrossRefADSGoogle Scholar
  69. 69.
    Jaeger, G., Ann, K.: Disentanglement and decoherence in a pair of qutrits under dephasing noise. J. Mod. Opt. 54(16–17), 2327 (2007)CrossRefADSGoogle Scholar
  70. 70.
    Xiao-San, M., Ming-Fan, R., Guang-Xing, Z., An-Min, W.: Dynamics of entanglement of qutrit-qutrit states with stochastic dephasing. Commun. Theor. Phys. 56(2), 258 (2011)CrossRefMATHADSGoogle Scholar
  71. 71.
    Karpat, G., Gedik, Z.: Invariant quantum discord in qubit–qutrit systems under local dephasing. Phys. Scr. 2013(T153), 014036 (2013)CrossRefGoogle Scholar
  72. 72.
    Bergli, J., Galperin, Y.M., Altshuler, B.L.: Decoherence in qubits due to low-frequency noise. New J. Phys. 11(2), 025002 (2009)CrossRefADSGoogle Scholar
  73. 73.
    Bordone, P., Buscemi, F., Benedetti, C.: Effect of Markov and non-Markov classical noise on entanglement dynamics. Fluctuat. Noise Lett. 11(03), 1242003 (2012)CrossRefGoogle Scholar
  74. 74.
    Faoro, L., Ioffe, L.B.: Microscopic origin of low-frequency flux noise in Josephson circuits. Phys. Rev. Lett. 100(22), 227005 (2008)CrossRefADSGoogle Scholar
  75. 75.
    Buscemi, F., Bordone, P.: Time evolution of tripartite quantum discord and entanglement under local and nonlocal random telegraph noise. Phys. Rev. A 87(4), 042310 (2013)CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Tsamouo Tsokeng Arthur
    • 1
  • Tchoffo Martin
    • 1
  • Lukong Cornelius Fai
    • 1
  1. 1.Mesoscopic and Multilayer Structures Laboratory, Department of Physics, Faculty of ScienceUniversity of DschangDschangCameroon

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