Skip to main content
SpringerLink
Log in

Comparative explorations of the revival and robustness for quantum dynamics under decoherence channels

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

In this paper, we demonstrate the revival and robustness of quantum dynamics under local decoherent evolutions through investigating the dynamical behaviors of quantum correlation. The results show that in depolarizing channel, quantum discord damps faster and revivals after a dark interval of time, while the others will revival immediately at the critical point. In addition, in hybrid channel the declining initial condition can speed up the attenuation of quantum discord within a limited time, while it can enable trace distance discord and Bures distance discord to damp more smoothly. In this sense, quantum discord is typically less robust against decoherence than the others. Interestingly, nonlocality shows different decay rates in the vicinity of critical point. Additionally, we lastly provide a physical interpretation concerning these phenomena.

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

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  MATH  Google Scholar 

  2. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  3. Vedral, V.: The role of relative entropy in quantum information theory. Rev. Mod. Phys. 74, 197 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. Raimond, J.M., Brune, M., Haroche, S.: Manipulating quantum entanglement with atoms and photons in a cavity. Rev. Mod. Phys. 73, 565 (2001)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Wei, T.C., Goldbart, P.M.: Geometric measure of entanglement and applications to bipartite and multipartite quantum states. Phys. Rev. A 68, 042307 (2003)

    Article  ADS  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  8. Shi, J.D., Wu, T., Song, X.K., Ye, L.: Quantum correlations of two spin-1 particles in the optical lattice. Int. J. Mod. Phys. B 28, 1450049 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  9. Modi, K., Brodutch, A., Cable, H., Paterek, T., Vedral, V.: The classical-quantum boundary for correlations: discord and related measures. Rev. Mod. Phys. 84, 1655 (2012)

    Article  ADS  Google Scholar 

  10. Piani, M., Gharibian, S., Adesso, G., Calsamiglia, J., Horodecki, P., Winter, A.: All nonclassical correlations can be activated into distillable entanglement. Phys. Rev. Lett. 106, 220403 (2011)

    Article  ADS  Google Scholar 

  11. Streltsov, A., Kampermann, H., Bruß, D.: Linking quantum discord to entanglement in a measurement. Phys. Rev. Lett. 106, 160401 (2011)

    Article  ADS  Google Scholar 

  12. Passante, G., Moussa, O., Trottier, D.A., Laflamme, R.: Experimental detection of nonclassical correlations in mixed-state quantum computation. Phys. Rev. A 84, 044302 (2011)

    Article  ADS  Google Scholar 

  13. Ali, M., Rau, A.R.P., Alber, G.: Quantum discord for two-qubit \(X\) states. Phys. Rev. A 81, 042105 (2010)

    Article  ADS  Google Scholar 

  14. Giorda, P., Paris, M.G.A.: Gaussian quantum discord. Phys. Rev. Lett. 105, 020503 (2010)

    Article  ADS  Google Scholar 

  15. Adesso, G., Datta, A.: Quantum versus classical correlations in Gaussian states. Phys. Rev. Lett. 105, 030501 (2010)

    Article  ADS  Google Scholar 

  16. 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)

    Article  ADS  Google Scholar 

  17. Paula, F.M., de Oliveira, T.R., Sarandy, M.S.: Geometric quantum discord through the Schatten 1-norm. Phys. Rev. A 87, 064101 (2013)

    Article  ADS  Google Scholar 

  18. Aaronson, B., Franco, R.L., Adesso, G.: Comparative investigation of the freezing phenomena for quantum correlations under nondissipative decoherence. Phys. Rev. A 88, 012120 (2013)

    Article  ADS  Google Scholar 

  19. Bell, J.S.: On the einstein podolsky rosen paradox. Physics 1, 195 (1964)

    Google Scholar 

  20. Scarani, V., Acín, A., Schenck, E., Aspelmeyer, M.: Nonlocality of cluster states of qubits. Phys. Rev. A 71, 042325 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. Shi, J.D., Wu, T., Song, X.K., Ye, L.: Dynamics of entanglement under decoherence in noninertial frames. Chin. Phys. B 23, 020310 (2014)

    Article  ADS  Google Scholar 

  22. Sen, A., Sarkar, D., Bhar, A.: Decoherence dynamics of measurement-induced nonlocality and comparison with geometric discord for two qubit systems. Quantum Inf. Process. 12, 3007–3022 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. Shi, J.D., Wu, T., Song, X.K., Ye, L.: Multipartite concurrence for \(X\) states under decoherence. Quantum Inf. Process. 13, 1405–1056 (2014)

    MATH  Google Scholar 

  24. Debarba, T., Maciel, T.O., Vianna, R.O.: Witnessed entanglement and the geometric measure of quantum discord. Phys. Rev. A 86, 024302 (2012)

    Article  ADS  Google Scholar 

  25. Nakano, T., Piani, M., Adesso, G.: Negativity of quantumness and its interpretations. Phys. Rev. A 88, 012117 (2013)

    Article  ADS  Google Scholar 

  26. Spehner, D., Orszag, M.: Geometric quantum discord with Bures distance. New J. Phys. 15, 103001 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. Bures, D.: An extension of Kakutani’s theorem on infinite product measures to the tensor product of semifinite w*-algebras. Trans. Am. Math. Soc. 135, 199 (1969)

    MathSciNet  MATH  Google Scholar 

  28. Vedral, V., Plenio, M.B.: Entanglement measures and purification procedures. Phys. Rev. A 57, 1619 (1998)

    Article  ADS  Google Scholar 

  29. Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880 (1969)

    Article  ADS  Google Scholar 

  30. Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V., Wehner, S.: Bell nonlocality. Rev. Mod. Phys. 86, 419 (2014)

    Article  ADS  Google Scholar 

  31. Horodecki, R., Horodecki, P., Horodecki, M.: Violating Bell inequality by mixed spin-1/2 states: necessary and sufficient condition. Phys. Lett. A 200, 340 (1995)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  32. Ren, B.C., Wei, H.R., Deng, F.G.: Correlation dynamics of a two-qubit system in a Bell-diagonal state under non-identical local noises. Quantum Inf. Process. 13, 1175–1189 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  33. Lang, M.D., Caves, C.M.: Quantum discord and the geometry of Bell-diagonal states. Phys. Rev. Lett. 105, 150501 (2010)

    Article  ADS  Google Scholar 

  34. Shi, J.D., Xu, S., Ma, W.C., Song, X.K., Ye, L.: Purifying two-qubit entanglement in nonidentical decoherence by employing weak measurements. Quantum Inf. Process 14, 1387–1397 (2015)

    Article  ADS  MATH  Google Scholar 

  35. Salles, A., de Melo, F., Almeida, M.P., Hor-Meyll, M., Walborn, S.P., Souto Ribeiro, P.H., Davidovich, L.: Experimental investigation of the dynamics of entanglement: sudden death, complementarity, and continuous monitoring of the environment. Phys. Rev. A 78, 022322 (2008)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Science Foundation of China under Grants Nos. 61275119, 11575001, and 11247256, and also by the fund of Anhui Provincial Natural Science Foundation (Grant No. 1508085QF139).

Author information

Authors and Affiliations

  1. School of Physics and Material Science, Anhui University, Hefei, 230601, China

    Jia-Dong Shi, Dong Wang & Liu Ye

Authors
  1. Jia-Dong Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dong Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Liu Ye
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Liu Ye.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shi, JD., Wang, D. & Ye, L. Comparative explorations of the revival and robustness for quantum dynamics under decoherence channels. Quantum Inf Process 15, 1649–1659 (2016). https://doi.org/10.1007/s11128-015-1233-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-015-1233-4

Keywords

Search

Navigation