[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Dynamics of relative entropy of coherence under Markovian channels

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

We study the relative entropy of coherence under the effect of certain one-qubit channels that are Markovian and noisy. The cohering power and decohering power of phase damping, amplitude damping, flip and depolarizing channels are analytically calculated. For phase damping channel, the decohering power on the \(x,\ y,\) and z bases is the same. The same phenomenon is observed for the flip and depolarizing channels. Further, we show that weak measurement and its reversal can be employed to suppress the decohering power of the amplitude damping channel.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Bartlett, S.D., Rudolph, T., Spekkens, R.W.: Reference frames, superselection rules, and quantum information. Rev. Mod. Phys. 79, 555 (2007)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. Marvian, I., Spekkens, R.W.: The theory of manipulations of pure state asymmetry: basic tools and equivalence classes of states under symmetric operations. New J. Phys. 15, 033001 (2013)

    Article  ADS  Google Scholar 

  3. Marvian, I., Spekkens, R.W.: Modes of asymmetry: the application of harmonic analysis to symmetric quantum dynamics and quantum reference frames. Phys. Rev. A 90, 062110 (2014)

    Article  ADS  Google Scholar 

  4. Lloyd, S.: Quantum coherence in biological systems. J. Phys. Conf. Ser. 302, 012037 (2011)

    Article  ADS  Google Scholar 

  5. Li, C.-M., Lambert, N., Chen, Y.-N., Chen, G.-Y., Nori, F.: Examining non-locality and quantum coherent dynamics induced by a common reservoir. Sci. Rep. 2, 885 (2012)

    ADS  Google Scholar 

  6. Lambert, N., Chen, Y.-N., Chen, Y.-C., Li, C.-M., Chen, G.-Y., Nori, F.: Quantum biology. Nat. Phys. 9, 10 (2013)

    Article  Google Scholar 

  7. Narasimhachar, V., Gour, G.: Low-temperature thermodynamics with quantum coherence. Nat. Commun. 6, 7689 (2015)

    Article  ADS  Google Scholar 

  8. Åberg, J.: Catalytic coherence. Phys. Rev. Lett. 113, 150402 (2014)

    Article  Google Scholar 

  9. Ćwikliński, P., Studziński, M., Horodecki, M., Oppenheim, J.: Towards fully quantum second laws of thermodynamics: limitations on the evolution of quantum coherences. Phys. Rev. Lett. 115, 210403 (2015)

    Article  Google Scholar 

  10. Plenio, M.B., Virmani, S.: An introduction to entanglement measures. Quantum Inf. Comput. 7, 1 (2007)

    MathSciNet  MATH  Google Scholar 

  11. Baumgratz, T., Cramer, M., Plenio, M.B.: Quantifying coherence. Phys. Rev. Lett. 113, 140401 (2014)

    Article  ADS  Google Scholar 

  12. Girolami, D.: Observable measure of quantum coherence in finite dimensional systems. Phys. Rev. Lett. 113, 170401 (2014)

    Article  ADS  Google Scholar 

  13. Streltsov, A., Singh, U., Dhar, H.S., Bera, M.N., Adesso, G.: Measuring quantum coherence with entanglement. Phys. Rev. Lett. 115, 020403 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  14. Shao, L.H., Xi, Z.J., Fan, H., Li, Y.M.: Fidelity and trace-norm distances for quantifying coherence. Phys. Rev. A 91, 042120 (2015)

    Article  ADS  Google Scholar 

  15. Yuan, X., Zhou, H.Y., Cao, Z., Ma, X.F.: Intrinsic randomness as a measure of quantum coherence. Phys. Rev. A 92, 022124 (2015)

    Article  ADS  Google Scholar 

  16. Xi, Z.J., Li, Y.M., Fan, H.: Quantum coherence and correlations in quantum system. Sci. Rep. 5, 10922 (2015)

    Article  ADS  Google Scholar 

  17. Hu, X.Y., Fan, H.: Coherence extraction from measurement-induced disturbance. arXiv:1508.01978 (2015)

  18. Napoli, C., Bromley, T.R., Cianciaruso, M., Piani, M., Johnston, N., Adesso, G.: Robustness of coherence: an operational and observable measure of quantum coherence. Phys. Rev. Lett. 116, 150502 (2016)

    Article  ADS  Google Scholar 

  19. Rana, S., Parashar, P., Lewenstein, M.: Trace-distance measure of coherence. Phys. Rev. A 93, 012110 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  20. Hu, X.Y., Milne, A., Zhang, B.Y., Fan, H.: Quantum coherence of steered states. Sci. Rep. 6, 19365 (2016)

    Article  ADS  Google Scholar 

  21. Hu, X.Y.: Coherence non-generating channels. arXiv:1604.00145 (2016)

  22. Liu, Z.W., Hu, X.Y., Lloyd, S.: A theory of resource destruction. arXiv:1606.03723 (2016)

  23. Winter, A., Yang, D.: Operational resource theory of coherence. Phys. Rev. Lett. 116, 120404 (2016)

    Article  ADS  Google Scholar 

  24. Singh, U., Bera, M.N., Misra, A., Pati, A.K.: Erasing quantum coherence: An operational approach. arXiv:1506.08186 (2015)

  25. Bromley, T.R., Cianciaruso, M., Adesso, G.: Frozen quantum coherence. Phys. Rev. Lett. 114, 210401 (2015)

    Article  ADS  Google Scholar 

  26. Mani, A., Karimipour, V.: Cohering and decohering power of quantum channels. Phys. Rev. A 92, 032331 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  27. Xi, Z.J., Hu, M.L., Li, Y.M., Fan, H.: Cohering power of unitary operations and de-cohering of quantum operations. arXiv:1510.06473 (2015)

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

    MATH  Google Scholar 

  29. Korotkov, A.N., Keane, K.: Decoherence suppression by quantum measurement reversal. Phys. Rev. A 81, 040103(R) (2010)

    Article  ADS  Google Scholar 

  30. Lee, J.-C., Jeong, Y.-C., Kim, Y.-S., Kim, Y.-H.: Experimental demonstration of decoherence suppression via quantum measurement reversal. Opt. Express 19, 16309 (2011)

    Article  ADS  Google Scholar 

  31. Kim, Y.-S., Lee, J.-C., Kwon, O., Kim, Y.-H.: Protecting entanglement from decoherence using weak measurement and quantum measurement reversal. Nat. Phys. 8, 117 (2012)

    Article  Google Scholar 

  32. Lee, J.-C., Lim, H.-T., Hong, K.-H., Jeong, Y.-C., Kim, M.S., Kim, Y.-H.: Experimental demonstration of delayed-choice decoherence suppression. Nat. Commun. 5, 4522 (2014)

    ADS  Google Scholar 

Download references

Acknowledgments

We are very grateful to the reviewers and the editors for their invaluable comments and detailed suggestions that helped to improve the quality of the present paper. This work was supported by NSFC under Grant Nos. 11504205, 61502179, 61472452, the Fundamental Research Funds of Shandong University under Grant No. 2014TB018, and the Natural Science Foundation of Guangdong Province of China under Grant No. 2014A030310265. H.Z. Situ was sponsored by the State Scholarship Fund of the China Scholarship Council.

Author information

Authors and Affiliations

  1. College of Mathematics and Informatics, South China Agricultural University, Guangzhou, 510642, China

    Haozhen Situ

  2. School of Information Science and Engineering, and Shandong Provincial Key Laboratory of Laser Technology and Application, Shandong University, Jinan, 250100, China

    Xueyuan Hu

Authors
  1. Haozhen Situ
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xueyuan Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Haozhen Situ.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Situ, H., Hu, X. Dynamics of relative entropy of coherence under Markovian channels. Quantum Inf Process 15, 4649–4661 (2016). https://doi.org/10.1007/s11128-016-1425-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-016-1425-6

Keywords

Search

Navigation