Advertisement

Dynamics of entropic uncertainty for atoms immersed in thermal fluctuating massless scalar field

  • Zhiming Huang
Article

Abstract

In this article, the dynamics of quantum memory-assisted entropic uncertainty relation for two atoms immersed in a thermal bath of fluctuating massless scalar field is investigated. The master equation that governs the system evolution process is derived. It is found that the mixedness is closely associated with entropic uncertainty. For equilibrium state, the tightness of uncertainty vanishes. For the initial maximum entangled state, the tightness of uncertainty undergoes a slight increase and then declines to zero with evolution time. It is found that temperature can increase the uncertainty, but two-atom separation does not always increase the uncertainty. The uncertainty evolves to different relatively stable values for different temperatures and converges to a fixed value for different two-atom distances with evolution time. Furthermore, weak measurement reversal is employed to control the entropic uncertainty.

Keywords

Entropic uncertainty Mixedness Dynamics Fluctuating massless scalar field Weak measurement reversal 

Notes

Acknowledgements

Z.M. Huang was supported by the Science Foundation for Young Teachers of Wuyi University (2015zk01) and the Doctoral Research Foundation of Wuyi University (2017BS07).

References

  1. 1.
    Heisenberg, W.: Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Z. Phys. 43, 172 (1927)ADSCrossRefzbMATHGoogle Scholar
  2. 2.
    Coles, P.J., Berta, M., Tomamichel, M., Wehner, S.: Entropic uncertainty relations and their applications. Rev. Mod. Phys. 89, 015002 (2017)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Kennard, E.H.: Zur Quantenmechanik einfacher Bewegungstypen. Z. Phys. 44, 326 (1927)ADSCrossRefzbMATHGoogle Scholar
  4. 4.
    Robertson, H.P.: The uncertainty principle. Phys. Rev. 34, 163 (1929)ADSCrossRefGoogle Scholar
  5. 5.
    Deutsch, D.: Uncertainty in quantum measurements. Phys. Rev. Lett. 50, 631 (1983)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    Kraus, K.: Complementary observables and uncertainty relations. Phys. Rev. D 35, 3070 (1987)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    Maassen, H., Uffnk, J.B.M.: Generalized entropic uncertainty relations. Phys. Rev. Lett. 60, 1103 (1988)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    Bialynicki-Birula, I.: Formulation of the uncertainty relations in terms of the Rényi entropies. Phys. Rev. A 74, 052101 (2006)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    Coles, P.J., Piani, M.: Improved entropic uncertainty relations and information exclusion relations. Phys. Rev. A 89, 022112 (2014)ADSCrossRefGoogle Scholar
  10. 10.
    Renes, J.M., Boileau, J.C.: Conjectured strong complementary information tradeoff. Phys. Rev. Lett. 103, 020402 (2009)ADSCrossRefGoogle Scholar
  11. 11.
    Berta, M., Christandl, M., Colbeck, R., Renes, J.M., Renner, R.: The uncertainty principle in the presence of quantum memory. Nat. Phys. 6, 659 (2010)CrossRefGoogle Scholar
  12. 12.
    Hu, M.L., Fan, H.: Quantum-memory-assisted entropic uncertainty principle, teleportation, and entanglement witness in structured reservoirs. Phys. Rev. A 86, 032338 (2012)ADSCrossRefGoogle Scholar
  13. 13.
    Zou, H.M., et al.: The quantum entropic uncertainty relation and entanglement witness in the two-atom system coupling with the non-Markovian environments. Phys. Scr. 89, 115101 (2014)ADSCrossRefGoogle Scholar
  14. 14.
    Hu, M.L., Fan, H.: Competition between quantum correlations in the quantum-memory-assisted entropic uncertainty relation. Phys. Rev. A 87, 022314 (2013)ADSCrossRefGoogle Scholar
  15. 15.
    Hu, M.L., Fan, H.: Upper bound and shareability of quantum discord based on entropic uncertainty relations. Phys. Rev. A 88, 014105 (2013)ADSCrossRefGoogle Scholar
  16. 16.
    Pati, A.K., et al.: Quantum discord and classical correlation can tighten the uncertainty principle in the presence of quantum memory. Phys. Rev. A 86, 042105 (2012)ADSCrossRefGoogle Scholar
  17. 17.
    Mondal, D., Pati, A.K.: Quantum speed limit for mixed states using an experimentally realizable metric. Phys. Lett. A 380, 1395 (2016)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Pires, D.P., Cianciaruso, M., Céleri, L.C., Adesso, G., Soares-Pinto, D.O.: Generalized geometric quantum speed limits. Phys. Rev. X 6, 021031 (2016)Google Scholar
  19. 19.
    Hall, M.J.W., Wiseman, H.M.: Heisenberg-style bounds for arbitrary estimates of shift parameters including prior information. New J. Phys. 14, 033040 (2012)ADSCrossRefGoogle Scholar
  20. 20.
    Tomamichel, M., Renner, R.: Uncertainty relation for smooth entropies. Phys. Rev. Lett. 106, 110506 (2011)ADSCrossRefGoogle Scholar
  21. 21.
    Coles, P.J., Colbeck, R., Yu, L., Zwolak, M.: Uncertainty relations from simple entropic properties. Phys. Rev. Lett. 108, 210405 (2012)ADSCrossRefGoogle Scholar
  22. 22.
    Berta, M., Wehner, S., Wilde, M.M.: Entropic uncertainty and measurement reversibility. New J. Phys. 18, 073004 (2016)ADSCrossRefGoogle Scholar
  23. 23.
    Adabi, F., Salimi, S., Haseli, S.: Tightening the entropic uncertainty bound in the presence of quantum memory. Phys. Rev. A 93, 062123 (2016)ADSCrossRefGoogle Scholar
  24. 24.
    Liu, S., Mu, L.Z., Fan, H.: Entropic uncertainty relations for multiple measurements. Phys. Rev. A 91, 042133 (2015)ADSCrossRefGoogle Scholar
  25. 25.
    Xu, Z.Y., Yang, W.L., Feng, M.: Quantum-memory-assisted entropic uncertainty relation under noise. Phys. Rev. A 86, 012113 (2012)ADSCrossRefGoogle Scholar
  26. 26.
    Wang, D., et al.: Entropic uncertainty relations for Markovian and non-Markovian processes under a structured bosonic reservoir. Sci. Rep. 7, 1066 (2017)ADSCrossRefGoogle Scholar
  27. 27.
    Wang, D., et al.: Exploration of quantum-memory-assisted entropic uncertainty relations in a noninertial frame. Laser Phys. Lett. 14, 055205 (2017)ADSCrossRefGoogle Scholar
  28. 28.
    Wang, D., et al.: Quantum-memory-assisted entropic uncertainty relation in a Heisenberg XYZ chain with an inhomogeneous magnetic field. Laser Phys. Lett. 14, 065203 (2017)ADSCrossRefGoogle Scholar
  29. 29.
    Huang, A.J., et al.: Exploring entropic uncertainty relation in the Heisenberg XX model with inhomogeneous magnetic field. Quantum Inf. Process. 16, 204 (2017)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Zhang, J.L., Yu, H.W.: Entanglement generation in atoms immersed in a thermal bath of external quantum scalar fields with a boundary. Phys. Rev. A. 75, 012101 (2007)ADSCrossRefGoogle Scholar
  31. 31.
    Zhang, J.L., Yu, H.W.: Unruh effect and entanglement generation for accelerated atoms near a reflecting boundary. Phys. Rev. D 75, 104014 (2007)ADSCrossRefGoogle Scholar
  32. 32.
    Jia, L.J., Tian, Z.H., Jing, J.L.: Entropic uncertainty relation in de Sitter space. Ann. Phys. 353, 37 (2015)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Hu, J.W., Yu, H.W.: Entanglement dynamics for uniformly accelerated two-level atoms. Phys. Rev. A 91, 012327 (2015)ADSMathSciNetCrossRefGoogle Scholar
  34. 34.
    Huang, Z.M., Situ, H.Z.: Dynamics of quantum correlation and coherence for two atoms coupled with a bath of fluctuating massless scalar feld. Ann. Phys. 377, 484 (2017)ADSCrossRefzbMATHGoogle Scholar
  35. 35.
    Zhang, S.Y., Fang, M.F., Yu, M.: Controlling of entropic uncertainty in qubits system under the generalized amplitude damping channel via weak measurements. Int. J. Theor. Phys. 55, 1824 (2016)CrossRefzbMATHGoogle Scholar
  36. 36.
    Wang, D., et al.: Entropic uncertainty for spin-1/2 XXX chains in the presence of inhomogeneous magnetic fields and its steering via weak measurement reversals. Laser Phys. Lett. 14, 095204 (2017)ADSCrossRefGoogle Scholar
  37. 37.
    Huang, A.J., Shi, J.D., Wang, D., Ye, L.: Steering quantum-memory-assisted entropic uncertainty under unital and nonunital noises via filtering operations. Quantum Inf. Process. 16, 46 (2017)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Yu, M., Fang, M.F.: Controlling the quantum-memory-assisted entropic uncertainty relation by quantum-jump-based feedback control in dissipative environments. Quantum Inf. Process. 16, 213 (2017)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  39. 39.
    Peters, N.A., Wei, T.C., Kwiat, P.G.: Mixed state sensitivity of several quantum information benchmarks. Phys. Rev. A 70, 052309 (2004)ADSCrossRefGoogle Scholar
  40. 40.
    Sun, Q., Al-Amri, M., Davidovich, L., Suhail, M.: Zubairy: Reversing entanglement change by a weak measurement. Phys. Rev. A 82, 052323 (2010)ADSCrossRefGoogle Scholar
  41. 41.
    Huang, Z.M., Zhang, C.: Protecting quantum correlation from correlated amplitude damping channel. Braz. J. Phys. 47, 400 (2017)ADSCrossRefGoogle Scholar
  42. 42.
    Huang, Z.M., Situ, H.Z.: Optimal protection of quantum coherence in noisy environment. Int. J. Theor. Phys. 56, 503 (2017)CrossRefzbMATHGoogle Scholar
  43. 43.
    Huang, Z.M., Rong, Z.B., Zou, X.F., Situ, H.Z., Zhao, L.H.: Protecting qutrit quantum coherence. Int. J. Theor. Phys. 56, 2540 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  44. 44.
    Gorini, V., Kossakowski, A., Surdarshan, E.C.G.: Completely positive dynamical semigroups of N-level systems. J. Math. Phys. 17, 821 (1976)ADSMathSciNetCrossRefGoogle Scholar
  45. 45.
    Lindblad, G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48, 119 (1976)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  46. 46.
    Breuer, H.-P., Petruccione, F.: The Theory of Open Quantum Systems. Oxford University Press, Oxford (2002)zbMATHGoogle Scholar
  47. 47.
    Huang, Z.M., Qiu, D.W., Mateus, P.: Geometry and dynamics of one-norm geometric quantum discord. Quantum Inf. Process. 15, 301 (2016)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  48. 48.
    Ali, M., Rau, A.R.P., Alber, G.: Quantum discord for two-qubit X states. Phys. Rev. A 81, 042105 (2010)ADSCrossRefGoogle Scholar
  49. 49.
    Chen, Q., Zhang, C., Yu, X., Yi, X.X., Oh, C.H.: Quantum discord of two-qubit X states. Phys. Rev. A 84, 042313 (2011)ADSCrossRefGoogle Scholar
  50. 50.
    Li, B., Wang, Z.X., Fei, S.M.: Quantum discord and geometry for a class of two-qubit states. Phys. Rev. A 83, 022321 (2011)ADSCrossRefGoogle Scholar
  51. 51.
    Jafari, R., Kargarian, M., Langari, A., Siahatgar, M.: Phase diagram and entanglement of the Ising model with Dzyaloshinskii–Moriya interaction. Phys. Rev. B 78, 214414 (2008)ADSCrossRefGoogle Scholar
  52. 52.
    Ma, F.W., Liu, S.X., Kong, X.M.: Quantum entanglement and quantum phase transition in the XY model with staggered Dzyaloshinskii–Moriya interaction. Phys. Rev. A 84, 042302 (2011)ADSCrossRefGoogle Scholar
  53. 53.
    Song, X.K., Wu, T., Ye, L.: Renormalization of quantum discord and Bell nonlocality in the XXZ model with Dzyaloshinskii–Moriya interaction. Ann. Phys. 349, 220 (2014)ADSCrossRefGoogle Scholar
  54. 54.
    Huang, Z.M.: Dynamics of quantum correlation and coherence in de Sitter universe. Quantum Inf. Process. 16, 207 (2017)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  55. 55.
    Huang, Z.M., Tian, Z.H.: Dynamics of quantum entanglement in de Sitter spacetime and thermal Minkowski spacetime. Nucl. Phys. B 923, 458 (2017)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  56. 56.
    Huang, Z.M., Tian, Z.H.: Dynamics of quantum correlation in de Sitter spacetime. J. Phys. Soc. Jpn. 86, 094003 (2017)ADSCrossRefGoogle Scholar
  57. 57.
    Huang, Z.M., Zhang, C., Zhang, W., Zhao, L.H.: Equivalence of quantum resource measures for X states. Int. J. Theor. Phys. 56, 3615 (2017)CrossRefzbMATHGoogle Scholar
  58. 58.
    Huang, Z.M., Situ, H.Z., Zhang, C.: Quantum coherence and correlation in spin models with Dzyaloshinskii–Moriya interaction. Int. J. Theor. Phys. 56, 2178 (2017)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.School of Economics and ManagementWuyi UniversityJiangmenChina

Personalised recommendations