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Entanglement Dynamics of a Two-qubit XYZ Spin Chain Under both Dzyaloshinskii-Moriya Interaction and Time-dependent Anisotropic Magnetic Field


In the present paper, the quantum entanglement dynamics of two qubits Heisenberg-XYZ spin chain under a time dependent magnetic field effects, and considering the Dzyaloshinskii-Moriya (DM) interactions is studied. Assuming the system as being influenced by a non-Markovian environment, the dynamics of entanglement through the concurrence is studied. It follows from the simulations that the time dependency character of the DM coupling, the external magnetic field, and the Heisenberg spin-spin coupling preserves longer entanglement in the system compared to the case with these parameters constant. Moreover, it also follows that the effects of the environment on the system induces the loss of entanglement and then, the time interval of entanglement sudden death highly depends on the initial state considered. It is also observed that by tuning the strength of the DM coupling associated with a time varying magnetic field and a time varying spin-spin anisotropic coupling, the system can be better protected from unwanted effects of the environment and thus, entanglement can be preserved for a longer period of time.

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  1. 1.

    Zheng, S.B., Guo, G.C.: Efficient scheme for two-atom entanglement and quantum information processing in cavity qed. Phys. Rev. Lett. 85(11), 2392 (2000)

    ADS  Google Scholar 

  2. 2.

    Chen, Y.H., Qin, W., Nori, F.: Fast and high-fidelity generation of steady-state entanglement using pulse modulation and parametric amplification. arXiv:1901.10249 (2019)

  3. 3.

    Chou, K.S., Blumoff, J.Z., Wang, C.S., Reinhold, P.C., Axline, C.J., Gao, Y.Y., Frunzio, L., Devoret, M.H., Jiang, L, Schoelkopf, R.J.: Deterministic teleportation of a quantum gate between two logical qubits. Nature 561(7723), 368–373 (2018)

    ADS  Google Scholar 

  4. 4.

    Takeda, S., Mizuta, T., Fuwa, M., Van Loock, P., Furusawa, A.: Deterministic quantum teleportation of photonic quantum bits by a hybrid technique. Nature 500(7462), 315–318 (2013)

    ADS  Google Scholar 

  5. 5.

    Krauter, H., Salart, D., Muschik, C.A., Petersen, J.M., Shen, H., Fernholz, T., Polzik, E.S.: Deterministic quantum teleportation between distant atomic objects. Nat. Phys. 9(7), 400–404 (2013)

    Google Scholar 

  6. 6.

    Ren, J.G., Xu, P., Yong, H.L., Zhang, L., Liao, S.K., Yin, J., Liu, W.Y., Cai, W.Q., Yang, M., Li L., et al.: Ground-to-satellite quantum teleportation. Nature 549(7670), 70 (2017)

    ADS  Google Scholar 

  7. 7.

    Streltsov, A., Adesso, G., Plenio, M.B.: Colloquium: quantum coherence as a resource. Rev. Mod. Phys. 89(4), 041003 (2017)

    ADS  MathSciNet  Google Scholar 

  8. 8.

    Vedral, V.: Quantum entanglement. Nat. Phys. 10(4), 256 (2014)

    Google Scholar 

  9. 9.

    Franco, R.L., Compagno, G.: Indistinguishability of elementary systems as a resource for quantum information processing. Phys. Rev. Lett. 120(24), 240403 (2018)

    Google Scholar 

  10. 10.

    Liu, X.S., Long, G.L., Tong, D.M., Li, F.: General scheme for superdense coding between multiparties. Phys. Rev. A 65(2), 022304 (2002)

    ADS  Google Scholar 

  11. 11.

    Ouellette, J.: Quantum key distribution. Industrial Physicist 10(6), 22–25 (2004)

    Google Scholar 

  12. 12.

    Murao, M., Jonathan, D., Plenio, M.B., Vedral, V.: Quantum telecloning and multiparticle entanglement. Phys. Rev. A 59(1), 156 (1999)

    ADS  Google Scholar 

  13. 13.

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

    ADS  Google Scholar 

  14. 14.

    Franco, R.L., D’Arrigo, A., Falci, G., Compagno, G., Paladino, E.: Preserving entanglement and nonlocality in solid-state qubits by dynamical decoupling. Phys. Rev. B 90(5), 054304 (2014)

    ADS  Google Scholar 

  15. 15.

    Nosrati, F., Mortezapour, A., Franco, R.L.: Validating and controlling quantum enhancement against noise by the motion of a qubit. Phys. Rev. A 101(1), 012331 (2020)

    ADS  Google Scholar 

  16. 16.

    Shor, P.W.: Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52(4), R2493 (1995)

    ADS  Google Scholar 

  17. 17.

    Sorelli, G., Leonhard, N., Shatokhin, V.N., Reinlein, C., Buchleitner, A.: Entanglement protection of high-dimensional states by adaptive optics. New J. Phys. 21(2), 023003 (2019)

    ADS  Google Scholar 

  18. 18.

    Palma, G.M., Suominen, K.A., Ekert, A.K.: Quantum computers and dissipation. In: Proceedings of the royal society of london a: mathematical, physical and engineering sciences, vol. 452, pp 567–584. The Royal Society (1996)

  19. 19.

    Rab, A.S., Polino, E., Man, Z.X., An, N.B., Xia, Y.J., Spagnolo, N., Franco, R. L., Sciarrino, F.: Entanglement of photons in their dual wave-particle nature. Nature Commun. 8(1), 1–7 (2017)

    Google Scholar 

  20. 20.

    Bellomo, B., Franco, R.L., Compagno, G.: N identical particles and one particle to entangle them all. Phys. Rev. A 96(2), 022319 (2017)

    ADS  Google Scholar 

  21. 21.

    Tchoffo, M., Fouokeng, G.C., Tendong, E., Fai, L.C.: Dzyaloshinshkii-Moriya interaction effects on the entanglement dynamics of a two qubit xxz spin system in non-markovian environment. J. Magn. Magn. Mater. 407, 358–364 (2016)

    ADS  Google Scholar 

  22. 22.

    Beenakker, C.W.J., van Houten, H.: Quantum transport in semiconductor nanostructures. Solid State Phys. 44, 1–228 (1991)

    Google Scholar 

  23. 23.

    Immanuel B.: Quantum coherence and entanglement with ultracold atoms in optical lattices. Nature 453(7198), 1016 (2008)

    Google Scholar 

  24. 24.

    Yamamoto, S., Fukui, T.: Thermodynamic properties of heisenberg ferrimagnetic spin chains: Ferromagnetic-antiferromagnetic crossover. Phys. Rev. B 57(22), R14008 (1998)

    ADS  Google Scholar 

  25. 25.

    Burns, W., Chen, C.L., Moeller, R.: Fiber-optic gyroscopes with broad-band sources. J. Lightwave Technol. 1(1), 98–105 (1983)

    ADS  Google Scholar 

  26. 26.

    Sharma, K.K.: Herring–flicker coupling and thermal quantum correlations in bipartite system. Quantum Inf. Process 17(11), 321 (2018)

    ADS  MathSciNet  MATH  Google Scholar 

  27. 27.

    Li, D.C., Cao, Z.L.: Thermal entanglement in the anisotropic Heisenberg XYZ model with different inhomogeneous magnetic fields. Opt Commun 282(6), 1226–1230 (2009)

    ADS  Google Scholar 

  28. 28.

    Inami, T., Konno, H.: Integrable XYZ spin chain with boundaries. J. Phys. A Math. General 27(24), L913 (1994)

    ADS  MathSciNet  MATH  Google Scholar 

  29. 29.

    Pinheiro, F., Bruun, G.M., Martikainen, J.P., Larson, J.: X y z quantum Heisenberg models with p-orbital bosons. Phys. Rev. Lett. 111(20), 205302 (2013)

    ADS  Google Scholar 

  30. 30.

    Peotta, S., Mazza, L., Vicari, E., Polini, M., Fazio, R., Rossini, D.: The XYZ chain with Dzyaloshinsky–Moriya interactions: from spin–orbit-coupled lattice bosons to interacting kitaev chains. J. Stat. Mech. Theory Exp. 2014(9), P09005 (2014)

    Google Scholar 

  31. 31.

    Luther, A.: Eigenvalue spectrum of interacting massive fermions in one dimension. Phys. Rev. B 14(5), 2153 (1976)

    ADS  Google Scholar 

  32. 32.

    Tôru, M.: Recent progress in the theory of itinerant electron magnetism. J. Magn. Magn. Mater. 14(1), 1–46 (1979)

    Google Scholar 

  33. 33.

    Dzyaloshinskii, I.E.: Theory of helicoidal structures in antiferromagnets. i. nonmetals. Sov. Phys. JETP 19(4), 960–971 (1964)

    Google Scholar 

  34. 34.

    Zhang, G.F.: Thermal entanglement and teleportation in a two-qubit Heisenberg chain with Dzyaloshinski-Moriya anisotropic antisymmetric interaction. Phys. Rev. A 75(3), 034304 (2007)

    ADS  Google Scholar 

  35. 35.

    Le, S., Guo-Hui, Y.: Quantum discord behavior about two-qubit Heisenberg XYZ model with decoherence. Chinese Phys. Lett. 31(3), 030304 (2014)

    Google Scholar 

  36. 36.

    Tanaś, R., Ficek, Z.: Stationary two-atom entanglement induced by nonclassical two-photon correlations. J. Opt. B Quantum and Semiclass. Opt. 6(6), S610 (2004)

    ADS  Google Scholar 

  37. 37.

    Orieux, A., d’Arrigo, A., Ferranti, G., Franco, R.L., Benenti, G., Paladino, E., Falci, G., Sciarrino, F., Mataloni, P.: Experimental on-demand recovery of entanglement by local operations within non-markovian dynamics. Sci. Rep. 5(1), 1–8 (2015)

    Google Scholar 

  38. 38.

    Dijkstra, A.G., Tanimura, Y.: Non-markovian entanglement dynamics in the presence of system-bath coherence. Phys. Rev. Lett. 104(25), 250401 (2010)

    ADS  Google Scholar 

  39. 39.

    Mortezapour, A., Naeimi, G., Franco, R.L.: Coherence and entanglement dynamics of vibrating qubits. Opt. Commun. 424, 26–31 (2018)

    ADS  Google Scholar 

  40. 40.

    Mundarain, D., Orszag, M.: Decoherence-free subspace and entanglement by interaction with a common squeezed bath. Phys. Rev. A 75(4), 040303 (2007)

    ADS  Google Scholar 

  41. 41.

    Al-Qasimi, A., James, D.F.V.: Sudden death of entanglement at finite temperature. Phys. Rev. A 77(1), 012117 (2008)

    ADS  Google Scholar 

  42. 42.

    Mazzola, L., Maniscalco, S., Piilo, J., Suominen, K.A., Garraway, B.M.: Sudden death and sudden birth of entanglement in common structured reservoirs. Phys. Rev. A 79(4), 042302 (2009)

    ADS  Google Scholar 

  43. 43.

    Henderson, L., Vedral, V.: Classical, quantum and total correlations. J. Phys. A Math General 34(35), 6899 (2001)

    ADS  MathSciNet  MATH  Google Scholar 

  44. 44.

    Qin, M., Ren, Z.Z.: Influence of intrinsic decoherence on entanglement teleportation via a heisenberg XYZ model with different dzyaloshinskii–Moriya interactions. Quantum Inf. Process 14(6), 2055–2066 (2015)

    ADS  MATH  Google Scholar 

  45. 45.

    Gurkan, Z.N., Pashaev, O.K.: Two qubit entanglement in magnetic chains with DM antisymmetric anisotropic exchange interaction. arXiv:0804.0710 (2008)

  46. 46.

    Sun, W.Y., Xu, S., Liu, C.C., Ye, L.: Negativity and quantum phase transition in the spin model using the quantum renormalization-group method. Int. J. Theor. Phys. 55(5), 2548–2557 (2016)

    MATH  Google Scholar 

  47. 47.

    Kamta, G.L., Starace, A.F.: Anisotropy and magnetic field effects on the entanglement of a two qubit heisenberg XY chain. Phys. Rev. Lett. 88(10), 107901 (2002)

    ADS  Google Scholar 

  48. 48.

    Yuan, X.Z., Goan, H.S., Zhu, K.D.: Influence of an external magnetic field on the decoherence of a central spin coupled to an antiferromagnetic environment. New J. Phys. 9(7), 219 (2007)

    ADS  Google Scholar 

  49. 49.

    Tchoffo, M., Fouokeng, G.C., Massou, S., Ngwa, E.A., Issofa, N., Fai, L.C., Tchouadeu, A.G., Kenné, J.P.: Effect of the variable B-field on the dynamic of a central electron spin coupled to an anti-ferromagnetic qubit bath (2012)

  50. 50.

    Bennett, C.H, DiVincenzo, D.P.: Quantum information and computation. Nature 404(6775), 247–255 (2000)

    ADS  MATH  Google Scholar 

  51. 51.

    Mintert, F.: Concurrence via entanglement witnesses. Phys. Rev. A 75(5), 052302 (2007)

    ADS  Google Scholar 

  52. 52.

    Wei, T.C., Nemoto, K., Goldbart, P.M., Kwiat, P.G., Munro, W.J., Verstraete, F.: Maximal entanglement versus entropy for mixed quantum states. Phys. Rev. A 67(2), 022110 (2003)

    ADS  Google Scholar 

  53. 53.

    DaeKil P.: Thermal entanglement and thermal discord in two-qubit Heisenberg XYZ chain with Dzyaloshinshkii–Moriya interactions. arXiv:1901.06165 (2019)

  54. 54.

    Guo, Y., Fang, M., Ke, Z.: Entropic uncertainty relation in a two-qutrit system with external magnetic field and dzyaloshinskii–moriya interaction under intrinsic decoherence. Quantum Inf. Process 17(7), 187 (2018)

    ADS  MathSciNet  MATH  Google Scholar 

  55. 55.

    Han, S.D., Tüfekċi, T., Spiller, T.P, Aydiner, E.: Entanglement in (1/2, 1) mixed-spin XY model with long-range interaction. Int. J. Theor. Phys. 56(5), 1474–1483 (2017)

    MATH  Google Scholar 

  56. 56.

    Man, Z.X., Xia, Y.J., Franco, R.L.: Cavity-based architecture to preserve quantum coherence and entanglement. Sci. Rep. 5, 13843 (2015)

    ADS  Google Scholar 

  57. 57.

    Breuer, H.P., Kappler, B., Petruccione, F.: Stochastic wave-function method for non-markovian quantum master equations. Phys. Rev. A 59(2), 1633 (1999)

    ADS  Google Scholar 

  58. 58.

    Mohammed, A.R., El-Shahat, T.M.: Study the entanglement dynamics of an anisotropic two-qubit heisenberg XYZ system in a magnetic field. J. Quantum Inf. Sci. 7(04), 160 (2017)

    Google Scholar 

  59. 59.

    Radhakrishnan, C., Parthasarathy, M., Jambulingam, S., Byrnes, T.: Quantum coherence of the Heisenberg spin models with Dzyaloshinsky-Moriya interactions. Sci. Rep. 7(1), 1–12 (2017)

    Google Scholar 

  60. 60.

    Tao, C., Chuan-Jia, S., Jin-Xing, L., Ji-Bing, L., Tang-Kun, L., Yan-Xia, H.: Decoherence effect in an anisotropic two-qubit Heisenberg XYZ model with inhomogeneous magnetic field. Commun. Theor. Phys. 53(6), 1053 (2010)

    ADS  MATH  Google Scholar 

  61. 61.

    Sadiek, G., Xu, Q., Kais, S.: Dynamics of entanglement in one and two-dimensional spin systems. arXiv:1304.5569 (2013)

  62. 62.

    Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V., Wehner, S.: Bell nonlocality. Rev. Mod. Phys. 86(2), 419 (2014)

    ADS  Google Scholar 

  63. 63.

    Bellomo, B., Franco, R.L., Compagno, G.: Entanglement dynamics of two independent qubits in environments with and without memory. Phys. Rev. A 77(3), 032342 (2008)

    ADS  Google Scholar 

  64. 64.

    Yang, H., Ding, Z.Y., Sun, W.Y., Ming, F., Wang, D., Zhang, C.J., Liu Y: Coherence visualizing bell-nonlocality and their interrelation for two-qubit X states in quantum steering ellipsoid formalism. Quantum Inf. Process 18(5), 146 (2019)

    ADS  Google Scholar 

  65. 65.

    Rau, A.R.P.: Algebraic characterization of x-states in quantum information. J Phys A Math Theoretical 42(41), 412002 (2009)

    MathSciNet  MATH  Google Scholar 

  66. 66.

    Wootters, W.K.: Entanglement of formation and concurrence. Quantum Inf. Comput. 1(1), 27–44 (2001)

    MathSciNet  MATH  Google Scholar 

  67. 67.

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

    ADS  MATH  Google Scholar 

  68. 68.

    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(1), 1–7 (2013)

    Google Scholar 

  69. 69.

    Yu, T., Eberly, J.H.: Sudden death of entanglement: classical noise effects. Opt. Commun. 264(2), 393–397 (2006)

    ADS  Google Scholar 

  70. 70.

    Aolita, L., De Melo, F., Davidovich, L.: Open-system dynamics of entanglement: a key issues review. Rep. Prog. Phys. 78(4), 042001 (2015)

    ADS  Google Scholar 

  71. 71.

    Yu, T., Eberly, J.H.: Sudden death of entanglement. Science 323(5914), 598–601 (2009)

    ADS  MathSciNet  MATH  Google Scholar 

  72. 72.

    Hamid, A.Z.: Random quantum discord in a mixed three-spin ising-XY model with added dzyaloshinshkii–moriya (DM) interaction. J. Korean Phys. Soc. 70(9), 835–844 (2017)

    Google Scholar 

  73. 73.

    Dehghani, A., Mojaveri, B., Bahrbeig, R.J., Nosrati, F., Franco, R.L.: Entanglement transfer in a noisy cavity network with parity-deformed fields. JOSA B 36(7), 1858–1866 (2019)

    ADS  Google Scholar 

  74. 74.

    DaeKil P.: Critical temperature of thermal entanglement phase transition in coupled harmonic oscillators. arXiv:1903.03297 (2019)

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Martin, T., Giresse, T.A. Entanglement Dynamics of a Two-qubit XYZ Spin Chain Under both Dzyaloshinskii-Moriya Interaction and Time-dependent Anisotropic Magnetic Field. Int J Theor Phys 59, 2232–2248 (2020).

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  • Qubits
  • Entanglement
  • Concurrence
  • Entanglement sudden death
  • Entanglement sudden birth