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International Journal of Theoretical Physics

, Volume 57, Issue 11, pp 3473–3479 | Cite as

Manipulating Einstein-Podolsky-Rosen Steering by Quantum-Jump-Based Feedback in Dissipative Environment

  • Zhiming Huang
Article

Abstract

In this paper, we investigate the behaviors of Einstein-Podolsky-Rosen (EPR) steering manipulated via quantum-jump-based feedback (QJBF) in noisy environment. We firstly derived the master equation that governs the system evolution. It is shown that the QJBF with an appropriate feedback parameter can preserve and generate the EPR steering destroyed by the dissipative environment. EPR steering quickly decays as dissipative time increases. For feedback parameter \(\lambda =\frac {\pi }{2}\), EPR steering oscillatorily develops to zero with evolution time, while entanglement decreases monotonously with decoherent time, so QJBF with feedback parameter \(\lambda =\frac {\pi }{2}\) can effectively protect EPR steering in some certain time.

Keywords

Einstein-Podolsky-Rosen steering Quantum-jump-based feedback Entanglement 

Notes

Acknowledgments

This work is supported by the Science Foundation for Young Teachers of Wuyi University (2015zk01) and the Doctoral Research Foundation of Wuyi University (2017BS07).

References

  1. 1.
    Schrödinger, E.: Discussion of probability relations between separated systems. Math. Proc. Camb. Phil. Soc. 31, 555 (1935)CrossRefADSGoogle Scholar
  2. 2.
    Schrödinger, E.: Probability relations between separated systems. Math. Proc. Camb. Phil. Soc. 32, 446 (1936)CrossRefADSGoogle Scholar
  3. 3.
    Skrzypczyk, P., Navascués, M., Cavalcanti, D.: Quantifying Einstein-Podolsky-Rosen steering. Phys. Rev. Lett. 112, 180404 (2014)CrossRefADSGoogle Scholar
  4. 4.
    Qin, Z.Z., Deng, X.W., Tian, C.X., Wang, M.H., Su, X.L., Xie, C.D., Peng, K.C.: Manipulating the direction of Einstein-Podolsky-Rosen steering. Phys. Rev. A 95, 052114 (2017)CrossRefADSGoogle Scholar
  5. 5.
    Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete?. Phys. Rev. 47, 777 (1935)CrossRefADSGoogle Scholar
  6. 6.
    Horst, B., Bartkiewicz, K., Miranowicz, A.: Two-qubit mixed states more entangled than pure states: Comparison of the relative entropy of entanglement for a given nonlocality. Phys. Rev. A 87, 042108 (2013)CrossRefADSGoogle Scholar
  7. 7.
    Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)MathSciNetCrossRefADSGoogle Scholar
  8. 8.
    Wiseman, H.M., Jones, S.J., Doherty, A. C.: Steering, entanglement, nonlocality, and the Einstein-Podolsky-Rosen paradox. Phys. Rev. Lett. 98, 140402 (2007)MathSciNetCrossRefADSGoogle Scholar
  9. 9.
    Cavalcanti, E.G., Jones, S.J., Wiseman, H.M., Reid, M.D.: Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox. Phys. Rev. A 80, 032112 (2009)CrossRefADSGoogle Scholar
  10. 10.
    Saunders, D.J., Jones, S.J., Wiseman, H.M., Pryde, G.J.: Experimental EPR-steering using Bell-local states. Nat. Phys. 6, 845 (2010)CrossRefGoogle Scholar
  11. 11.
    Wittmann, B., Ramelow, S., Steinlechner, F., Langford, N.K., Brunner, N., Wiseman, H.M., Ursin, R., Zeilinger, A.: Loophole-free einsteinCPodolskyCRosen experiment via quantum steering. New J. Phys. 14, 053030 (2012)CrossRefADSGoogle Scholar
  12. 12.
    Sun, K., Xu, J.-S., Ye, X.-J., Wu, Y.-C., Chen, J.-L., Li, C.-F., Guo, G.-C.: Experimental demonstration of the Einstein-Podolsky-Rosen steering game based on the all-versus-nothing proof. Phys. Rev. Lett. 113, 140402 (2014)CrossRefADSGoogle Scholar
  13. 13.
    Wollmann, S., Walk, N., Bennet, A.J., Wiseman, H.M., Pryde, G.J.: Observation of genuine one-way Einstein-Podolsky-Rosen steering. Phys. Rev. Lett. 116, 160403 (2016)CrossRefADSGoogle Scholar
  14. 14.
    Sun, K., Ye, X., Xu, J., Xu, X., Tang, J., Wu, Y., Chen, J., Li, C., Guo, G.: Experimental quantification of asymmetric EinsteinPodolsky-Rosen steering. Phys. Rev. Lett. 116, 160404 (2016)CrossRefADSGoogle Scholar
  15. 15.
    Branciard, C., Cavalcanti, E.G., Walborn, S.P., Scarani, V., Wiseman, H.M.: One-sided device-independent quantum key distribution: security, feasibility, and the connection with steering. Phys. Rev. A 85, 010301 (2012)CrossRefADSGoogle Scholar
  16. 16.
    Gehring, T., et al.: Implementation of continuous-variable quantum key distribution with composable and one-sided-deviceindependent security against coherent attacks. Nat. Commun. 6, 8795 (2015)CrossRefGoogle Scholar
  17. 17.
    Piani, M., Watrous, J.: Necessary and sufficient quantum information characterization of Einstein-Podolsky-Rosen steering. Phys. Rev. Lett. 114, 060404 (2015)MathSciNetCrossRefADSGoogle Scholar
  18. 18.
    He, Q., Rosales-Zárate, L., Adesso, G., Reid, M.D.: Secure continuous variable teleportation and Einstein-Podolsky-Rosen Steering. Phys. Rev. Lett. 115, 180502 (2015)CrossRefADSGoogle Scholar
  19. 19.
    Walborn, S.P., Salles, A., Gomes, R.M., Toscano, F., Souto Ribeiro, P. H.: Revealing hidden Einstein-Podolsky-Rosen nonlocality. Phys. Rev. Lett. 106, 130402 (2011)CrossRefADSGoogle Scholar
  20. 20.
    Schneeloch, J., Broadbent, C.J., Walborn, S.P., Cavalcanti, E.G., Howell, J.C.: Einstein-podolsky-rosen steering inequalities from entropic uncertainty relations. Phys. Rev. A 87, 062103 (2013)CrossRefADSGoogle Scholar
  21. 21.
    Zhen, Y.Z., Zheng, Y.L., Cao, W. F., Li, L., Chen, Z. B., Liu, N. L., Chen, K.: Certifying Einstein-Podolsky-Rosen steering via the local uncertainty principle. Phys. Rev. A 93, 012108 (2016)CrossRefADSGoogle Scholar
  22. 22.
    Hu, X. Y., Fan, H.: Effect of local channels on quantum steering ellipsoids. Phys. Rev. A 91, 022301 (2015)CrossRefADSGoogle Scholar
  23. 23.
    Banik, M., Das, S., Majumdar, A. S.: Measurement incompatibility and channel steering. Phys. Rev. A 91, 062124 (2015)CrossRefADSGoogle Scholar
  24. 24.
    Kiukas, J., Burgarth, J.D.: Quantum resource control for noisy Einstein-Podolsky-Rosen steering with qubit measurements. Phys. Rev. A 93, 032107 (2016)CrossRefADSGoogle Scholar
  25. 25.
    Sun, W.Y., Wang, D., Shi, J.D., Ye, L.: Exploration quantum steering, nonlocality and entanglement of two-qubit X-state in structured reservoirs. Sci. Rep. 7, 39651 (2017)CrossRefADSGoogle Scholar
  26. 26.
    Hu, M.L., Fan, H.: Evolution equation for geometric quantum correlation measures. Phys. Rev. A 91, 052311 (2015)CrossRefADSGoogle Scholar
  27. 27.
    Hu, M.L., Fan, H.: Evolution equation for quantum coherence. Sci. Rep. 6, 29260 (2016)CrossRefADSGoogle Scholar
  28. 28.
    Wiseman, H.M., Milburn, G.J.: Quantum theory of optical feedback via homodyne detection. Phys. Rev. Lett. 70, 548 (1993)CrossRefADSGoogle Scholar
  29. 29.
    Wiseman, H.M.: Quantum theory of continuous feedback. Phys. Rev. A 49, 2133 (1994)CrossRefADSGoogle Scholar
  30. 30.
    Carvalho, A.R.R., Reid, A.J.S., Hope, J.J.: Controlling entanglement by direct quantum feedback. Phys. Rev. A 78, 012334 (2008)CrossRefADSGoogle Scholar
  31. 31.
    Wang, J., Wiseman, H.M., Milburn, G.J.: Dynamical creation of entanglement by homodyne-mediated feedback. Phys. Rev. A 71, 042309 (2005)CrossRefADSGoogle Scholar
  32. 32.
    Carvalho, A.R.R., Hope, J.J.: Stabilizing entanglement by quantum-jump-based feedback. Phys. Rev. A 76(R), 010301 (2007)MathSciNetCrossRefADSGoogle Scholar
  33. 33.
    Li, J.G., Zou, J., Shao, B., Cai, J. F.: Steady atomic entanglement with different quantum feedbacks. Phys. Rev. A 77, 012339 (2008)CrossRefADSGoogle Scholar
  34. 34.
    Ganesan, N., Tarn, T.J.: Decoherence control in open quantum system via classical feedback. Phys. Rev. A 75, 032323 (2007)CrossRefADSGoogle Scholar
  35. 35.
    Sun, H.Y., Shu, P. L., Li, C., Yi, X.X.: Feedback control on geometric phase in dissipative two-level systems. Phys. Rev. A 79, 022119 (2009)CrossRefADSGoogle Scholar
  36. 36.
    Zheng, Q., Ge, L., Yao, Y., Zhi, Q. J.: Enhancing parameter precision of optimal quantum estimation by direct quantum feedback. Phys. Rev. A 91, 033805 (2015)CrossRefADSGoogle Scholar
  37. 37.
    Yu, M., Fang, M.F.: Steady and optimal entropy squeezing of a two-level atom with quantum-jump-based feedback and classical driving in a dissipative cavity. Quantum Inf. Process. 15, 4175 (2016)CrossRefADSGoogle 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)MathSciNetCrossRefADSGoogle Scholar
  39. 39.
    Costa, A.C.S., Angelo, R.M.: Quantification of Einstein-Podolski-Rosen steering for two-qubit states. Phys. Rev. A 93(R), 020103 (2016)CrossRefADSGoogle Scholar
  40. 40.
    Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245 (1998)CrossRefADSGoogle Scholar
  41. 41.
    Huang, Z.M., Situ, H.Z.: Dynamics of quantum correlation and coherence for two atoms coupled with a bath of fluctuating massless scalar field. Ann. Phys. 377, 484 (2017)CrossRefADSGoogle Scholar
  42. 42.
    Ali, M., Rau, A.R.P., Alber, G.: Quantum discord for two-qubit X states. Phys. Rev. A 81, 042105 (2010)CrossRefADSGoogle Scholar
  43. 43.
    Huang, Z.M., Qiu, D.W., Mateus, P.: Geometry and dynamics of one-norm geometric quantum discord. Quantum Inf. Process. 15, 301 (2016)MathSciNetCrossRefADSGoogle Scholar
  44. 44.
    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)CrossRefADSGoogle Scholar
  45. 45.
    Huang, Z.M.: Dynamics of quantum correlation and coherence in de Sitter universe. Quantum Inf. Process. 16, 207 (2017)MathSciNetCrossRefADSGoogle Scholar
  46. 46.
    Ma, F.W., Liu, S.X., Kong, X.: Quantum entanglement and quantum phase transition in the XY model with staggered Dzyaloshinskii-Moriya interaction. Phys. Rev. A 84, 042302 (2011)CrossRefADSGoogle Scholar
  47. 47.
    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)CrossRefGoogle Scholar
  48. 48.
    Huang, Z.M., Tian, Z.H.: Dynamics of quantum entanglement in de Sitter spacetime and thermal Minkowski spacetime. Nucl. Phys. B 923, 458 (2017)MathSciNetCrossRefADSGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.School of Economics and ManagementWuyi UniversityJiangmenChina

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