Skip to main content
SpringerLink
Log in

Decoherence and quantum steering of accelerated qubit–qutrit system

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

The bidirectional steerability between different-size subsystems is discussed for a single parameter accelerated qubit–qutrit system. The decoherence due to the mixing and acceleration parameters is investigated, where for the total system and the qutrit, it increases as the mixing parameter increases, while it decreases for the qubit. The non-classical correlations are quantified by using the local quantum uncertainty, where the uncertainty increases at large values of the acceleration parameter. The possibility that each subsystem steers each other is studied, where the behavior of the steering inequality predicts that the qubit has a large ability to steer the qutrit. The degree of steerability decays gradually when the qubit is accelerated. However, it decays suddenly when the qutrit or both subsystems are accelerated. The degree of steerability is shown for the qutrit vanishes at small values of the acceleration, while the qubit at large acceleration. The difference between the degrees of steerability depends on the initial state settings and the size of the accelerated subsystem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Data availability

Data sharing is not applicable to this article as no data sets were generated or analyzed during the current study.

References

  1. Einstein, A., Podolsky, B., Rosen, N.: Can quantum mechanical description of physical reality be considered complete. Phys. Rev. 47, 10 (1935)

    Article  MATH  Google Scholar 

  2. Schrödinger, E.: Discussion of probability relations between separated systems. In: Mathematical Proceedings of the Cambridge Philosophical Society, vol. 31 (1935)

  3. Wiseman, H.M., Jones, S.J., Doherty, A.C.: Steering, entanglement, nonlocality, and the Einstein–Podolsky–Rosen paradox. Phys. Rev. Lett. 98, 140402 (2007)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. Quintino, M.T., Vértesi, T., Cavalcanti, D., Augusiak, R., Demianowicz, M., Acín, A., Brunner, N.: Equivalence of entanglement, steering, and Bell nonlocality for general measurements. Phys. Rev. A 92, 032107 (2015)

    Article  ADS  Google Scholar 

  5. Šupić, I., Bowles, J.: Self-testing of quantum systems: a review. Quantum 4, 337 (2020)

    Article  Google Scholar 

  6. He, Q., Rosales-Zárate, L., Adesso, G., Reid, M.D.: Continuous variable teleportation and Einstein–Podolsky–Rosen steering. Phys. Rev. Lett. 115, 180502 (2015)

    Article  ADS  Google Scholar 

  7. Passaro, E., Cavalcanti, D., Skrzypczyk, P., Acín, A.: Optimal randomness certification in the quantum steering and prepare-and-measure scenarios. New J. Phys. 17, 11 (2015)

    Article  MATH  Google Scholar 

  8. 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)

    Article  ADS  Google Scholar 

  9. Ou, Z.Y., Pereira, S.F., Kimble, H.J., Peng, K.C.: Realization of the Einstein–Podolsky–Rosen paradox for continuous variables. Phys. Rev. Lett. 68, p3663 (1992)

    Article  ADS  Google Scholar 

  10. Smith, D.H., Gillett, G., De Almeida, M.P., Branciard, C., Fedrizzi, A., Weinhold, T.J., Lita, A., Calkins, B., Gerrits, T., Wiseman, H.M., et al.: Conclusive quantum steering with superconducting transition-edge sensors. Nat. Commun. 3, 1 (2012)

    Article  Google Scholar 

  11. Nguyen, H.C., Vu, T.: Necessary and sufficient condition for steerability of two-qubit states by the geometry of steering outcomes. Europhys. Lett. 115(1), 10003 (2016)

    Article  Google Scholar 

  12. 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(1), p1 (2017)

    ADS  Google Scholar 

  13. Metwally, N.: Steering information in quantum network. In: 3rd Smart Cities Symposium (SCS 2020) (2021)

  14. Meng Wang, Yu., Xiang, Q.H., Gong, Q.: Asymmetric quantum network based on multipartite Einstein–Podolsky–Rosen steering. JOSA B 32, 4 (2015)

    Google Scholar 

  15. Chen, L., Zhang, Y.Q.: Quantum steering in magnetic Heisenberg models at finite temperature. EPL Europhys. Lett. 120, 6 (2018)

    ADS  Google Scholar 

  16. Li, H.-Z., Han, R.-S., Zhang, Y.-Q., Chen, L.: Quantum steering in Heisenberg models with Dzyaloshinskii–Moriya interactions. Chin. Phys. B 27, 12 (2018)

    Article  Google Scholar 

  17. Liu, T., Wang, J., Jing, J., Fan, H.: The influence of Unruh effect on quantum steering for accelerated two-level detectors with different measurements. Ann. Phys. 390, p334 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  18. Wang, F., Xu, J., Cheng, G.L., Oh, C.H.: Generation of one-way Einstein–Podolsky–Rosen steering using interference-controlled asymmetric dissipation process. Ann. Phys. 388, 162–172 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  19. Huang, T.W.Y.B.Z., Dongwu, W., Zhang, W.: Steering entropic uncertainty of qutrit system. Mod. Phys. Lett. A 35(16), 2050127 (2020)

    Article  ADS  MATH  Google Scholar 

  20. Zhao, Z.L.F., Ye, L.: Improving of steering and nonlocality via local filtering operation in Heisenberg XY model. Mod. Phys. Lett. A 35(28), 2050233 (2020)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. Sun, W.-Y., Wang, D., Ding, Z.-Y., Ye, L.: Recovering the lost steerability of quantum states within non-markovian environments by utilizing quantum partially collapsing measurements. Laser Phys. Lett. 14, 12 (2017)

    Article  Google Scholar 

  22. Shu-Min, W., Li, Z.-C., Zeng, H.-S.: Quantum steering between two accelerated parties. Laser Phys. Lett. 17, 3 (2020)

    Google Scholar 

  23. Deng, X., Liu, Y., Wang, M., Su, X., Peng, K.: Sudden death and revival of Gaussian Einstein–Podolsky–Rosen steering in noisy channels. npj-Quantum Inf. 7, 1–8 (2021)

    Article  Google Scholar 

  24. Lin, W., Liao, C.G.: Enhancement of asymmetric steering via interference effects induced by twofold modulations in a cavity optomechanical system. Eur. Phys. J. Plus 36(3), 1–9 (2021)

    ADS  MathSciNet  Google Scholar 

  25. 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)

    Article  ADS  Google Scholar 

  26. Kogias, I., Skrzypczyk, P., Cavalcanti, D., Acín, A., Adesso, G.: Hierarchy of steering criteria based on moments for all bipartite quantum systems. Phys. Rev. Lett. 115, 210401 (2015)

    Article  ADS  Google Scholar 

  27. Żukowski, M., Dutta, A., Yin, Z.: Geometric Bell-like inequalities for steering. Phys. Rev. A 91, 032107 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  28. Peña-Armendáriz, T., Alarcón, R.R., Rosales-Zárate, L.E.C.: Continuous variable tripartite entanglement and steering using a third-order nonlinear optical interaction. JOSA B 382, 371–378 (2021)

    Article  ADS  Google Scholar 

  29. Cavalcanti, E.G., Foster, C.J., Fuwa, M., Wiseman, H.M.: Analog of the Clauser–Horne–Shimony–Holt inequality for steering. JOSA B 32(4), A74–A81 (2015)

    Article  ADS  Google Scholar 

  30. Ruzbehani, M.: Simulation of the Bell inequality violation based on quantum steering concept. Sci. Rep. 11, 1 (2021)

    Google Scholar 

  31. Riccardi, A., Macchiavello, C., Maccone, L.: Tight entropic uncertainty relations for systems with dimension three to five. Phys. Rev. A 95, 032109 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  32. Bruschi, A.E., Louko, J., Martín-Martínez, E., Dragan, A., Fuentes, I.: Unruh effect in quantum information beyond the single-mode approximation. Phys. Rev. A 82, 042332 (2010)

    Article  ADS  Google Scholar 

  33. Sun, W.-Y., Wang, D., Ye, L.: How relativistic motion affects Einstein–Podolsky–Rosen steering. Laser Phys. Lett. 14, 9 (2017)

    Article  Google Scholar 

  34. Li, Z.-C., Zeng, H.-S.: Quantum steering and its asymmetry of open quantum systems in accelerated frames. Euro Phys J. Plus 135, 1 (2020)

    Article  ADS  Google Scholar 

  35. Metwally, N.: Enhancing entanglement, local and non-local information of accelerated two-qubit and two-qutrit systems via weak-reverse measurements. EPL Europhys. Lett. 116(6), 60006 (2017)

    Article  ADS  Google Scholar 

  36. Fang, Y., Liu, X., Wang, J., Tian, Z., Jing, J.: Gaussian interferometric power in the localized two-mode gaussian states. Quantum Inf. Process. 18(8), 1–13 (2019)

    Article  Google Scholar 

  37. Zeng, H.-S., Cao, H.-M.: Distribution and evolution of quantum coherence for open multi-qubit systems in non-inertial frames. Annalen der Physik 533(4), 2000606 (2021)

    Article  ADS  MathSciNet  Google Scholar 

  38. Abd-Rabbou, M.Y., Metwally, N., Ahmed, M.M.A., Obada, A.-S.F.: Suppressing the information losses of accelerated qubit–qutrit system. Int. J. Quant. Inf. 17(04), 1950032 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  39. Lian, Y.-J., Liu, J.-M.: Quantum Fisher information of a qubit–qutrit system Garfinkler–Horowitz–Strominger dilation space-time. Commun. Theor. Phys. 73, 085102 (2021)

    Article  ADS  Google Scholar 

  40. Abd-Rabbou, M.Y., Metwally, N., Ahmed, M.M.A., Obada, A.-S.F.: Wigner function of noisy accelerated two-qubit system. Quantum Inf. Process. 18, 12 (2019)

    Article  MathSciNet  Google Scholar 

  41. Brivio, D., Cialdi, S., Vezzoli, S., Gebrehiwot, B.T., Genoni, M.G., Olivares, S., Paris, M.G.A.: Experimental estimation of one-parameter qubit gates in the presence of phase diffusion. Phys. Rev. A 81, 012305 (2010)

    Article  ADS  Google Scholar 

  42. Teklu, B., Olivares, S., Paris, M.G.A.: Bayesian estimation of one-parameter qubit gates. J. Phys. B At. Mol. Opt. Phys 42, 035502 (2009)

    Article  ADS  Google Scholar 

  43. Teklu, B., Genoni, M.G., Olivares, S., Paris, M.G.A.: Phase estimation in the presence of phase diffusion: the qubit case. Phys. Scr. 2010, 014062 (2010)

    Article  Google Scholar 

  44. Blok, M.S., Ramasesh, V.V., Schuster, T., O’Brien, K., Kreikebaum, J., Dahlen, D., Morvan, A., Yoshida, B., Yao, N.Y., Siddiqi, I.: Quantum information scrambling on a superconducting qutrit processor. Phys. Rev. X 11, 021010 (2021)

    Google Scholar 

  45. Fu, Y., Liu, W., Ye, X., Wang, Y., Zhang, C., Duan, C., Rong, X., Du, J.: Experimental investigation of quantum correlations in a two-qutrit spin system. Phys. Rev. Lett. 129, 100501 (2022)

    Article  ADS  Google Scholar 

  46. Tabia, G.N.M.: Experimental scheme for qubit and qutrit symmetric informationally complete positive operator-valued measurements using multiport devices. Phys. Rev. A 86, 062107 (2012)

    Article  ADS  Google Scholar 

  47. Guo, J.-L., Li, H., Long, G.-L.: Decoherent dynamics of quantum correlations in qubit–qutrit systems. Quantum Inf. Process. 12(11), 3421 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  48. Alsing, P.M., Fuentes-Schuller, I., Mann, R.B., Tessier, T.E.: Entanglement of Dirac fields in noninertial frames. Phys. Rev. A 74, 032326 (2006)

    Article  ADS  Google Scholar 

  49. Martín-Martínez, E., LuisGaray, J., León, J.: Quantum entanglement produced in the formation of a black hole. Phys. Rev. D 82, 064028 (2010)

    Article  ADS  Google Scholar 

  50. León, J., Martín-Martínez, E.: Spin and occupation number entanglement of Dirac fields for noninertial observers. Phys. Rev. A 20, 012314 (2009)

    Article  ADS  Google Scholar 

  51. Metwally, N.: Entanglement of simultaneous and non-simultaneous accelerated qubit–qutrit systems. Quantum Inf. Comput. 16(5–6), 530–542 (2016)

    MathSciNet  Google Scholar 

  52. Doukas, J., Brown, E.G., Dragan, A., Mann, R.B.: Entanglement and discord: accelerated observations of local and global modes. Phys. Rev. A 87, 012306 (2013)

    Article  ADS  Google Scholar 

  53. Zurek, W.H., Habib, S., Paz, J.P.: Coherent states via decoherence. Phys. Rev. Lett. 70, 1187–1190 (1993)

    Article  ADS  Google Scholar 

  54. Von Neumann, J.: Mathematical Foundations of Quantum Mechanics. Princeton University Press, Princeton (2018)

    Book  Google Scholar 

  55. Girolami, D., Tufarelli, T., Adesso, G.: Characterizing nonclassical correlations via local quantum uncertainty. Phys. Rev. A 110, 240402 (2013)

    Google Scholar 

  56. Kurzyński, P., Kołodziejski, A., Laskowski, W., Markiewicz, M.: Three-dimensional visualization of a qutrit. Phys. Rev. A 93, 062126 (2016)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank the referee for their reports which have improved the manuscript.

Author information

Authors and Affiliations

  1. Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, 11884, Cairo, Egypt

    M. Y. Abd-Rabbou, M. M. A. Ahmed & A.-S. F. Obada

  2. Department of Mathematics, College of Science, University of Bahrain, 32038, Zallaq, Bahrain

    N. Metwally

  3. Department of Mathematics, Aswan University, Aswan, 81528, Sahari, Egypt

    N. Metwally

Authors
  1. M. Y. Abd-Rabbou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. Metwally
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. M. A. Ahmed
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A.-S. F. Obada
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. Metwally.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Abd-Rabbou, M.Y., Metwally, N., Ahmed, M.M.A. et al. Decoherence and quantum steering of accelerated qubit–qutrit system. Quantum Inf Process 21, 363 (2022). https://doi.org/10.1007/s11128-022-03711-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-022-03711-6

Keywords

Search

Navigation