Advertisement

Entropic uncertainty relation in a two-qutrit system with external magnetic field and Dzyaloshinskii–Moriya interaction under intrinsic decoherence

Article

Abstract

In this paper, we explore the dynamic behaviors of entropic uncertainty relation in a two-qutrit system which is in the presence of external magnetic field and Dzyaloshinskii–Moriya (DM) interaction under intrinsic decoherence. The effects of the isotropic bilinear interaction, the external magnetic field, the DM interaction strength, as well as the intrinsic decoherence on the entropic uncertainty relation have been demonstrated in detail. Compared with previous results, our results show that, controlling the isotropic bilinear interaction parameter J, the external magnetic field strength \(B_{0}\), the DM interaction parameter D can result in inflation of the uncertainty, while increasing the intrinsic decoherence parameter can lift the uncertainty of the measurement. In particularly, under certain conditions (e.g., parameters J, \(B_{0}\) and D are large enough), the entropic uncertainty will ultimately tend to a stable value and be immune to decoherence.

Keywords

Entropic uncertainty relation Dzyaloshinskii-Moriya interaction Intrinsic decoherence 

Notes

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant Nos. 11747107 and 11374096), the Natural Science Foundation of Hunan Province (Grant No. 2017JJ3346), the Scientific Research Project of Hunan Province Department of Education (Grant No. 16C0134), the Project of Science and Technology Plan of Changsha (K1705022) and the Start-up Funds for Talent Introduction and Scientific Research of Changsha University 2015 (Grant No. SF1504).

References

  1. 1.
    Heisenberg, W.: The actual content of quantum theoretical kinematics and mechanics. Z. Phys. 43, 172 (1927)ADSCrossRefMATHGoogle Scholar
  2. 2.
    Robertson, H.P.: The uncertainty principle. Phys. Rev. 34, 163 (1929)ADSCrossRefGoogle Scholar
  3. 3.
    Deutsch, D.: Uncertainty in quantum measurements. Phys. Rev. Lett 50, 631C633 (1983)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Maassen, H., Uffink, J.B.M.: Generalized entropic uncertainty relations. Phys. Rev. Lett. 60, 1103 (1988)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    Renes, J.M., Boileau, J.C.: Physical underpinnings of privacy. Phys. Rev. A 78, 032335 (2008)ADSCrossRefGoogle Scholar
  6. 6.
    Renes, J.M., Boileau, J.C.: Conjectured strong complementary information tradeoff. Phys. Rev. Lett. 103, 020402 (2009)ADSCrossRefGoogle Scholar
  7. 7.
    Berta, M., Christandl, M., Colbeck, R., Renes, J.M., Renner, R.: The uncertainty principle in the presence of quantum memory. Nat. Phys 6, 659C662 (2010)CrossRefGoogle Scholar
  8. 8.
    Prevedel, R., Hamel, D.R., Colbeck, R., Fisher, K., Resch, K.J.: Experimental investigation of the uncertainty principle in the presence of quantum memory and its application to witnessing entanglement. Nat. Phys. 7, 757 (2011)CrossRefGoogle Scholar
  9. 9.
    Li, C.F., Xu, J.S., Xu, X.Y., Li, K., Guo, G.C.: Experimental investigation of the entanglement-assisted entropic uncertainty principle. Nat. Phys. 7, 752 (2011)CrossRefGoogle Scholar
  10. 10.
    Coles, P.J., Berta, M., Tomamichel, M., Wehner, S.: Entropic uncertainty relations and their applications. Rev. Mod. Phys. 89, 015002 (2017)ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    Tomamichel, M., Renner, R.: Uncertainty relation for smooth entropies. Phys. Rev. Lett. 106, 110506 (2011)ADSCrossRefGoogle Scholar
  12. 12.
    Coles, P.J., Colbeck, R., Yu, L., Zwolak, M.: Uncertainty relations from simple entropic properties. Phys. Rev. Lett. 108, 210504 (2012)CrossRefGoogle Scholar
  13. 13.
    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
  14. 14.
    Feng, J., Zhang, Y.Z., Gould, M.D., Fan, H.: Entropic uncertainty relations under the relativistic motion. Phys. Rev. B 726, 527–532 (2013)MATHGoogle Scholar
  15. 15.
    Hu, Y.D., Zhang, S.B., Wang, D., Ye, L.: Entropic uncertainty relation under dissipative environments and its steering by local non-unitary operations. Int. J. Theor. Phys. 55, 4641 (2016)CrossRefMATHGoogle Scholar
  16. 16.
    Wang, D., Huang, A.J., Ming, F., Sun, W.Y., Liu, H.P., Liu, C.C., Ye, L.: Quantum-memory-assisted entropic uncertainty relation in a Heisenberg XYZ chain with an inhomogeneous magnetic field. Laser Phys. Lett. 14, 065203 (2017)ADSCrossRefGoogle Scholar
  17. 17.
    Xiao, Y.L., Jing, N.H., Li-Jost, X.Q.: Uncertainty under quantum measures and quantum memory. Quantum. Inf. Pro. 16, 104 (2017)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    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)ADSMathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Zhang, J., Zhang, Y., Yu, C.S.: Entropic uncertainty relation and information exclusion relation for multiple measurements in the presence of quantum memory. Sci. Rep. 5, 11701 (2015)ADSCrossRefGoogle Scholar
  20. 20.
    Zhang, Y.L., Fang, M.F., Kuang, G.D., Zhou, Q.P.: Reducing quantum-memory-assisted entropic uncertainty by weak measurement and weak measurement reversal. Int. J. Quantum Inf. 13, 1550037 (2015)CrossRefMATHGoogle Scholar
  21. 21.
    Yao, C.M., Chen, Z.H., Ma, Z.G., Severini, S.: Serafini, A: entanglement and discord assisted entropic uncertainty relations under decoherence. Sci. China 57, 1703–1711 (2014)CrossRefGoogle Scholar
  22. 22.
    Huang, A.J., Wang, D., Wang, J.M., Shi, J.D., Sun, W.Y., Ye, L.: Exploring entropic uncertainty relation in the Heisenberg XX model with inhomogeneous magnetic field. Quantum Inf. Process. 16, 204 (2017)ADSMathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Wang, D., Ming, F., Huang, A.J., Sun, W.Y., Shi, J.D., Ye, L.: Exploration of quantum-memory-assisted entropic uncertainty relations in a noninertial frame. Laser Phys. Lett. 14, 055205 (2017)ADSCrossRefGoogle Scholar
  24. 24.
    Zheng, X., Zhang, G.F.: The effects of mixedness and entanglement on the properties of the entropic uncertainty in Heisenberg model with Dzyaloshinski–Moriya interaction. Quantum. Inf. Pro. 16, 1 (2017)ADSMathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    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, 090501 (2006)ADSCrossRefGoogle Scholar
  26. 26.
    Bourennane, M., Karlsson, A., Bjrk, G.: Quantum key distribution using multilevel encoding. Phys. Rev. A 64, 012306 (2001)ADSCrossRefGoogle Scholar
  27. 27.
    Cerf, N.J., Bourennane, M., Karlsson, A., Gisin, N.: Security of quantum key distribution using d-level systems. Phys. Rev. Lett. 88, 127902 (2002)ADSCrossRefGoogle Scholar
  28. 28.
    Durt, T., Cerf, N.J., Gisin, N., Zukowski, M.: Security of quantum key distribution with entangled B qutrits. Phys. Rev. A 67, 012311 (2003)ADSCrossRefGoogle Scholar
  29. 29.
    Dzyaloshinsky, I.: A thermodynamic theory of weak ferromagnetism of antiferromagnetics. J. Phys. Chem. Solid. 4, 241–255 (1958)ADSCrossRefGoogle Scholar
  30. 30.
    Moriya, T.: Anisotropic superexchange interaction and weak ferromagnetism. Phys. Rev. 120, 91–98 (1960)ADSCrossRefGoogle Scholar
  31. 31.
    Milburn, G.J.: Intrinsic decoherence in quantum mechanics. Phys. Rev. A 44, 5401 (1991)ADSCrossRefGoogle Scholar
  32. 32.
    Xu, J.B., Zou, X.B.: Dynamic algebraic approach to the system of a three-level atom in the configuration. Phys. Rev. A 60, 4743 (1999)ADSCrossRefGoogle Scholar
  33. 33.
    Liu, B.Q., Shao, B., Zou, J.: Tripartite states Bell-nonlocality sudden death with intrinsic decoherence. Phys. Lett. A 374, 1970–1974 (2010)ADSMathSciNetCrossRefMATHGoogle Scholar
  34. 34.
    Xu, Z.Y., Yang, W.L., Feng, M.: Quantum-memory-assisted entropic uncertainty relation under noise. Phys. Rev. A 86, 012113 (2012)ADSCrossRefGoogle Scholar
  35. 35.
    Riccardi, A., Macchiavello, C., Maccone, L.: Tight entropic uncertainty relations for systems with dimension three to five. Phys. Rev. A 95, 032109 (2017)ADSMathSciNetCrossRefGoogle Scholar
  36. 36.
    Man’ko, V.I., Marmo, G., Porzio, A., Solimeno, S., Ventriglia, F.: Homodyne estimation of quantum state purity by exploiting the covariant uncertainty relation. Phys. Scr. 83, 045001 (2011)ADSCrossRefMATHGoogle Scholar
  37. 37.
    Pati, A.K., Wilde, M.M., Devi, A.R.U., Rajagopal, A.K.: Sudha: Quantum discord and classical correlation can tighten the uncertainty principle in the presence of quantum memory. Phys. Rev. A 86, 042105 (2012)ADSCrossRefGoogle Scholar
  38. 38.
    Hu, M.L., Fan, H.: Upper bound and shareability of quantum discord based on entropic uncertainty relations. Phys. Rev. A 88, 014105 (2012)ADSCrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Department of Electronic and Communication EngineeringChangsha UniversityChangshaPeople’s Republic of China
  2. 2.Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, and Department of PhysicsHunan Normal UniversityChangshaPeople’s Republic of China

Personalised recommendations