Skip to main content
Log in

Intrinsic decoherence effects on measurement-induced nonlocality

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

By considering an exactly solvable model of a two interacting spin-1/2 qubits described by the Heisenberg anisotropic interaction in the presence of intrinsic decoherence, we study the dynamics of entanglement quantified by the concurrence and measurement-induced nonlocality (MIN) based on Hilbert–Schmidt norm and trace distance with different initial conditions. We highlight the relationship between the entanglement and MIN for the pure initial state. For an initial separable state, it is found that the robustness and the generation of the quantum correlations depend on the physical parameters. While considering the entangled state as an initial state, the results show that despite the phase decoherence, all the correlations reach their steady state values after exhibiting some oscillations. We reveal that the enhancement of correlations may occur by adjusting the strength of the Dzyaloshinskii–Moriya (DM) interaction and the intervention of the magnetic field decrease the quantum correlations. Finally, we show the existence of quantum correlations captured by MIN in the unentangled state.

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

Access this article

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

Similar content being viewed by others

References

  1. Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)

    Article  ADS  Google Scholar 

  2. Schrodinger, E.: Discussion of probability relations between separated systems. Proc. Camb. Philos. Soc. 31, 555 (1935)

    Article  ADS  Google Scholar 

  3. Nielsen, M., Chuang, I.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2010)

    Book  Google Scholar 

  4. Knill, E., Laflamme, R.: Power of one bit of quantum information. Phys. Rev. Lett. 81, 5672 (1998)

    Article  ADS  Google Scholar 

  5. Datta, A., Flammia, S.T., Caves, C.M.: Entanglement and the power of one qubit. Phys. Rev. A 72, 042316 (2005)

    Article  ADS  Google Scholar 

  6. Datta, A., Shaji, A., Caves, C.M.: Quantum discord and the power of one qubit. Phys. Rev. Lett. 100, 050502 (2008)

    Article  ADS  Google Scholar 

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

    ADS  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  12. Xiong, S., Zhang, W.J., Yu, C.-S., Song, H.-S.: Uncertainty-induced nonlocality. Phys. Lett. A 378, 344 (2014)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  14. Chang, L., Luo, S.: Remedying the local ancilla problem with geometric discord. Phys. Rev. A 87, 062303 (2013)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  18. Li, L., Wang, Q.-W., Shen, S.-Q., Li, M.: Measurement-induced nonlocality based on Wigner–Yanase skew information. EPL 114, 10007 (2016)

    Article  ADS  Google Scholar 

  19. Muthuganesan, R., Chandrasekar, V.K.: Affinity based measurement-induced nonlocality. Commun. Theor. Phys. 72, 075103 (2020)

    Article  ADS  Google Scholar 

  20. Bussandri, D.G., Majtey, A.P., Hernández, A.V.: Non-commutative measure of quantum correlations under local operations. Quantum Inf. Process 18, 47 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  21. Milburn, G.J.: Intrinsic decoherence in quantum mechanics. Phys. Rev. A 44, 5401 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  22. Moya-Cessa, H., et al.: Intrinsic decoherence in the atom-field interaction. Phys. Rev. A 48, 3900 (1993)

    Article  ADS  Google Scholar 

  23. Hill, S., Wootters, W.K.: Entanglement of a pair of quantum bits. Phys. Rev. Lett. 78, 5022 (1997)

    Article  ADS  Google Scholar 

  24. Dzyaloshinskii, I.: A thermodynamic theory of weak ferromagnetism of antiferromagnetics. J. Phys. Chem. Solids 4, 241 (1958)

    Article  ADS  Google Scholar 

  25. Moriya, T.: Anisotropic superexchange interaction and weak ferromagnetism. Phys. Rev. 120, 91 (1960)

    Article  ADS  Google Scholar 

  26. Ozaydin, F., Altintas, A.A.: Quantum Metrology: Surpassing the shot-noise limit with Dzyaloshinskii–Moriya interaction. Sci. Rep. 5, 16360 (2015)

    Article  ADS  Google Scholar 

  27. Sharma, K.K., Pande, S.N.: Entanglement dynamics in two-parameter qubit-qutritstates under Dzyaloshinskii–Moriya interaction. Quantum Inf. Process 13, 2017 (2014)

    Article  ADS  Google Scholar 

  28. Sharma, K.K., Pande, S.N.: Robustness of Greenberger–Horne–Zeilinger and W-states against Dzyaloshinskii–Moriya interaction. Quantum Inf. Process 15, 4995 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  29. Sharma, K.K., Pande, S.N.: Dzyaloshinskii–Moriya interaction as an agent to free the bound entangled states. Quantum Inf. Process 15, 1539 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  30. Sharma, K.K., Pande, S.N.: Dynamics of entanglement in qubit-qutrit with x-component of DM interaction. Commun. Theor. Phys. 65, 278 (2016)

    Article  ADS  Google Scholar 

  31. Yurischev, M.A.: On the quantum discord of general X states. Quantum Inf. Process 14, 3399 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  32. Yu, T., Eberly, J.H.: Sudden death of entanglement. Science 293, 5914 (2009)

    MathSciNet  MATH  Google Scholar 

  33. Muthuganesan, R., Sankaranarayanan, R.: Dynamics of measurement-induced nonlocality. Quantum Inf. Process 17, 305 (2018)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work has been financially supported by the Council of Scientific and Industrial Research (CSIR), Government of India under Grant No. 03(1444)/18/EMR-II.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to R. Muthuganesan.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Muthuganesan, R., Chandrasekar, V.K. Intrinsic decoherence effects on measurement-induced nonlocality. Quantum Inf Process 20, 46 (2021). https://doi.org/10.1007/s11128-020-02985-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-020-02985-y

Keywords

Navigation