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Quantum nonlocality in the spin-s Heisenberg models with the Dzyaloshinskii–Moriya interaction

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Abstract

Various measures of quantum nonlocality have been recently proposed. In this work, four indicators of measurement-induced nonlocality are studied for quantum thermal state with various couplings and temperatures in the spin-s Heisenberg models with the Dzyaloshinskii–Moriya interaction. Analytic and numerical calculations are presented for two cases of \(\hbox {s}=1/2\) and 1. It is shown that four indicators display similar behaviors at lower temperature. However, they have turning points at different couplings for a finite temperature. Remarkably, one or two indicators can increase, while others decrease as couplings or temperature enhances. The difference of nonlocality between two spin models is discussed. Those are helpful to further understand quantum nonlocality in the mixed states and to establish a proper measure of nonlocality.

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References

  1. Piani, N., Horodecki, P., Horodecki, R.: No-local-broadcasting theorem for multipartite quantum correlations. Phys. Rev. Lett. 100, 090502 (2008)

    Article  ADS  Google Scholar 

  2. Luo, S., Zhang, Q.: Superadditivity of Wigner–Yanase–Dyson information revisited. J. Stat. Phys. 131, 1169 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  3. Li, N., Luo, S.: Classical states versus separable states. Phys. Rev. A 78, 024303 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  4. Bell, J., et al.: On the Einstein–Podolsky–Rosen paradox. Physics 1, 195 (1964)

    Article  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  7. Vidral, V.: The role of relative entropy in quantum information theory. Rev. Mod. Phys. 74, 197 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  8. Horodecki, R., et al.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  9. Vutha, A.C., Bohr, E.A., Ransford, A., Campbell, W.C., Hamilton, P.: Displacement operators: the classical face of their quantum phase. Eur. J. Phys. 39, 025405 (2018)

    Article  Google Scholar 

  10. Hou, X.W., Chen, J.H., Ma, Z.Q.: Dynamical entanglement of vibrations in an algebraic model. Phys. Rev. A 74, 062513 (2006)

    Article  ADS  Google Scholar 

  11. Zhai, L., Zheng, Y.: Intramolecular energy transfer, entanglement, and decoherence in molecular systems. Phys. Rev. A 88, 012504 (2013)

    Article  ADS  Google Scholar 

  12. Arnesen, M.C., Bose, S., Vedral, V.: Natural thermal and magnetic entanglement in the 1D Heisenberg model. Phys. Rev. Lett. 87, 017901 (2001)

    Article  ADS  Google Scholar 

  13. Wang, X.: Threshold temperature for pairwise and many-particle thermal entanglement in the isotropic Heisenberg model. Phys. Rev. A 66, 044305 (2002)

    Article  ADS  Google Scholar 

  14. Zvyagin, A.A.: Thermal entanglement of spin chains with quantum critical behavior. Phys. Rev. B. 80, 144408 (2009)

    Article  ADS  Google Scholar 

  15. Zhang, G.F., et al.: Thermal entanglement in two qutrits system. Eur. Phys. J. D 32, 409 (2005)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  18. Piani, M., Gharibian, S., Adesso, G., Calsamiglia, J., Horodecki, P., Winter, A.: All nonclassical correlations can be activated into distillable entanglement. Phys. Rev. Lett. 106, 220403 (2011)

    Article  ADS  Google Scholar 

  19. Datta, A., Gharibian, S.: Signatures of nonclassicality in mixed-state quantum computation. Phys. Rev. A 79, 042325 (2009)

    Article  ADS  Google Scholar 

  20. Roa, L., Retamal, J.C., Alid-Vaccarezza, M.: Dissonance is required for assisted optimal state discrimination. Phys. Rev. Lett. 107, 080401 (2011)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  22. Ali, M., Rau, A., Alber, G.: Quantum discord for two-qubit X states. Phys. Rev. A 81, 042105 (2010); ibid., 82, 069902(E) (2010)

  23. Huang, Y.: Quantum discord for two-qubit X states: analytical formula with very small worst-case error. Phys. Rev. A 88, 014302 (2013)

    Article  ADS  Google Scholar 

  24. Girolami, D., Adesso, G.: Interplay between computable measures of entanglement and other quantum correlations. Phys. Rev. A 84, 052110 (2011)

    Article  ADS  Google Scholar 

  25. Adesso, G., Datta, A.: Quantum versus classical correlations in gaussian states. Phys. Rev. Lett. 105, 030501 (2010)

    Article  ADS  Google Scholar 

  26. Passante, G., Moussa, O., Laflamme, R.: Measuring geometric quantum discord using one bit of quantum information. Phys. Rev. A 84, 042313 (2011)

    Article  Google Scholar 

  27. Lu, X.M., Ma, J., Wang, X.: Optimal measurements to access classical correlations of two-qubit states. Phys. Rev. A 83, 012327 (2011)

    Article  ADS  Google Scholar 

  28. Dakić, B., Vedral, V., Brukner, C.: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502 (2010)

    Article  ADS  Google Scholar 

  29. Piani, M.: Problem with geometric discord. Phys. Rev. A 86, 034101 (2012)

    Article  ADS  Google Scholar 

  30. Tufarelli, T., et al.: Quantum resources for hybrid communication via qubit-oscillator states. Phys. Rev. A 86, 052326 (2012)

    Article  ADS  Google Scholar 

  31. Paula, F.M., de Oliveira, T.R., Sarandy, M.S.: Geometric quantum discord through the Schatten 1-norm. Phys. Rev. A 87, 064101 (2013)

    Article  ADS  Google Scholar 

  32. Ferraro, A., et al.: Almost all quantum states have nonclassical correlations. Phys. Rev. A 81, 052318 (2010)

    Article  ADS  Google Scholar 

  33. Obando, P.C., Paula, F.M., Sarandy, M.S.: Trace-distance correlations for X states and the emergence of the pointer basis in Markovian and non-Markovian regimes. Phys. Rev. A 92, 032307 (2015)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  35. Xu, P., Hu, Y.H., Hou, X.W.: Thermal quantum coherence and correlations in a spin-1 Heisenberg model. Phys. A 491, 282 (2018)

    Article  MathSciNet  Google Scholar 

  36. Rau, A.R.P.: Calculation of quantum discord in higher dimensions for X- and other specialized states. Quant. Inf. Proc. 17, 216 (2018)

    Article  MathSciNet  Google Scholar 

  37. Luo, S., Fu, S.: Measurement-induced nonlocality. Phys. Rev. Lett. 106, 120401 (2011)

    Article  ADS  Google Scholar 

  38. Sen, A., Sarkar, D., bhar, A.: Monogamy of measurement-induced nonlocality. J. Phys. A 45, 405306 (2012)

    Article  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  40. Muthuganesan, R., Sankaranarayanan, R.: Fidelity based measurement induced nonlocality. Phys. Rev. A 381, 3028 (2017)

    MATH  Google Scholar 

  41. Xi, Z., Wang, X., Li, Y.: Measurement-induced nonlocality based on the relative entropy. Phys. Rev. A 85, 042325 (2012)

    Article  ADS  Google Scholar 

  42. Hu, M.L., Fan, H.: Measurement-induced nonlocality based on the trace norm. New J. Phys. 17, 033004 (2015)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  44. Peters, N.A., Barreiro, J.T.: Remote state preparation: arbitrary remote control of photon polarization. Phys. Rev. Lett. 94, 150502 (2005)

    Article  ADS  Google Scholar 

  45. Muthuganesan, R., Sankaranarayanan, R.: Dynamics of measurement-induced nonlocality under decoherence. Quant. Inf. Proc. 17, 305 (2018)

    Article  Google Scholar 

  46. Yip, S.K.: Dimer state of spin-1 bosons in an optical lattice. Phys. Rev. Lett. 90, 250402 (2003)

    Article  ADS  Google Scholar 

  47. Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 88 (2008)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  49. Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in Fortran 77: The Art of Scientific Computing. Cambridge University Press, Cambridge (1986)

    MATH  Google Scholar 

  50. Streltsov, A., Kampermann, H., Bruß, D.: Linking quantum discord to entanglement in a measurement. Phys. Rev. Lett. 106, 160401 (2011)

    Article  ADS  Google Scholar 

  51. Rana, S., Parashar, P.: Comment on “Witnessed entanglement and the geometric measure of quantum discord”. Phys. Rev. A 87, 016301 (2013)

    Article  ADS  Google Scholar 

  52. Aaronson, B., Franco, R.L., Compagno, G., Adesso, G.: Hierarchy and dynamics of trace distance correlations. New J. Phys. 15, 093022 (2013)

    Article  ADS  Google Scholar 

  53. Montealegre, J.D., Paula, F.M., Saguia, A., Sarandy, M.S.: One-norm geometric quantum discord under decoherence. Phys. Rev. A 87, 042115 (2013)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  55. Milivojevic, M., Stepannenko, D.: Effective spin Hamiltonian of a gated tripe quantum dot in the presence of spin-orbit interaction. J. Phys. Condens. Matter 29, 405302 (2017)

    Article  Google Scholar 

  56. Kaszlikowski, D., Gnaciski, P., Zukowski, 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, 4418 (2000)

    Article  ADS  Google Scholar 

  57. Guo, J.L., Mi, Y.J., Zhang, J., Song, H.S.: Thermal quantum discord of spins in an inhomogeneous magnetic field. J. Phys. B. 44, 065504 (2011)

    Article  ADS  Google Scholar 

  58. Hu, Z., Wang, Y.C., Hou, X.W.: Thermal quantum correlations in a two-qubit Heisenberg XYZ model with different magnetic fields. Int. J. Quant. Inf. 13, 1550046 (2015)

    Article  MathSciNet  Google Scholar 

  59. Maziero, J., Celeri, L.C., Serra, R.M.: Classical and quantum correlations under decoherence. Phys. Rev. A 80, 044102 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  60. Fanchini, F.F., Werlang, T., Brasil, C.A.: Non-Markovian dynamics of quantum discord. Phys. Rev. A 81, 052107 (2012)

    Article  ADS  Google Scholar 

  61. Wei, T.C., et al.: Maximal entanglement versus entropy for mixed quantum states. Phys. Rev. A 67, 022110 (2003)

    Article  ADS  Google Scholar 

  62. Li, Z.J., et al.: Time evolution and transfer of entanglement between an isolated atom and a Jaynes–Cummings atom. J. Phys. B 40, 3401 (2007)

    Article  Google Scholar 

  63. Hou, X.W., Wan, M.F., Ma, Z.Q.: Entropy and negativity of Fermi-resonance coupling vibrations in a spectroscopic Hamiltonian. Phys. Rev. A 79, 022308 (2009)

    Article  ADS  Google Scholar 

  64. Yuan, Y.L., Hou, X.W.: Thermal geometric discords in a two-qutrit system. Int. J. Quant. Inf. 14, 1650016 (2016)

    Article  Google Scholar 

  65. Kheirandish, F., Akhtarshenas, S.J., Mohammadi, H.: Effect of spin-orbit interaction on entanglement of two-qubit Heisenberg XYZ systems in an inhomogeneous magnetic field. Phys. Rev. A 77, 042309 (2008)

    Article  ADS  Google Scholar 

  66. Liu, B.Q., Shao, B., Li, J.G., Zou, J., Wu, L.A.: Quantum and classical correlations in the one-dimensional XY model with Dzyaloshinskii-Moriya interaction. Phys. Rev. A 83, 052112 (2011)

    Article  ADS  Google Scholar 

  67. Sha, Y.T., Wang, Y., Sun, Z.H., Hou, X.W.: Thermal quantum coherence and correlation in the extended XY spin chain. Ann. Phys. 392, 229 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  68. Li, S.P., Sun, Z.H.: Local and intrinsic quantum coherence in critical systems. Phys. Rev. A 98, 022317 (2018)

    Article  ADS  Google Scholar 

  69. He, Y.J., Zhou, J., Li, S.P., Sun, Z.H.: Quantum coherence as indicators of quantum phase transitions, factorization and thermal phase transitions in the anisotropic XY model. Quant. Inf. Proc. 17, 320 (2018)

    Article  MathSciNet  Google Scholar 

  70. Bhattacharya, S., Banerjee, S., Pati, A.K.: Evolution of coherence and non-classicality under global environmental interaction. Quant. Inf. Proc. 17, 236 (2018)

    Article  MathSciNet  Google Scholar 

  71. Liu, T.W., He, Z.Y., Hou, X.W.: Dynamics of quantum correlations for three-qubit states in a noisy environment. Int. J. Mod. Phys. B 33, 1950145 (2019)

    Article  ADS  MathSciNet  Google Scholar 

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Acknowledgements

The authors thank the referees for valuable suggestions.

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  1. Department of Physics, Huazhong Normal University, Wuhan, 430079, China

    Yu-Xin Ma, Long Li & Xi-Wen Hou

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  1. Yu-Xin Ma
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Ma, YX., Li, L. & Hou, XW. Quantum nonlocality in the spin-s Heisenberg models with the Dzyaloshinskii–Moriya interaction. Quantum Inf Process 18, 288 (2019). https://doi.org/10.1007/s11128-019-2402-7

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