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Maximal Coherence in a Pre-Selected Basis

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Abstract

Since quantum coherence is viewed as a valuable resource for quantum information processing, its quantification and application has long been a topic of concern. And in framework of a resource theory of quantum coherence, quantum coherence is a basis-dependent quantity. Accordingly, when a basis is selected ahead of time, a natural question is raised: not all one-qubit systems can evolve to the maximally coherent state, so what determines the coherence of a system can evolve to the maximum? Base on the parameters of Hamiltonian we propose a criterion by which one can easily judge whether the coherence of one-qubit system can evolve to the maximum. Moreover, we show commutation relation between the operators for observation corresponding to pre-selected basis and Hamiltonian can be used to judge whether coherence of one-qubit system can evolve to the maximum.

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References

  1. Bennett, C.H., Brassard, G., Crepeau, C.: Phys. Rev. Lett. 70, 1895 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  2. Giovannetti, V., Lloyd, S., Maccone, L.: Nat. Photon. 5, 222 (2011)

    Article  ADS  Google Scholar 

  3. Imamog, A., Awschalom, D.D., Burkard, G.: Phys. Rev. Lett. 83, 4204 (2015)

    Article  ADS  Google Scholar 

  4. Xi, Z., Li, Y., Fan, H.: Sci. Rep. 5, 10922 (2015)

    Article  ADS  Google Scholar 

  5. Northup, T.E., Blatt, R.: Nat. Photon. 8, 356 (2014)

    Article  ADS  Google Scholar 

  6. Pan, F., Qiu, L., Liu, Z.: Sci. Rep. 7, 43919 (2017)

    Article  ADS  Google Scholar 

  7. Yoneda, J., Takeda, K., Otsuka, T.: Nat. Nanotech. 13, 102 (2018)

    Article  ADS  Google Scholar 

  8. Yu, C.S.: Phys. Rev. A 95, 042337 (2017)

    Article  ADS  Google Scholar 

  9. Sang, M., Nie, L.: Int. J. Theor. Phys. 56, 3638 (2017)

    Article  Google Scholar 

  10. Bai, C.M., Li, Y.M.: Int. J. Theor. Phys. 71, 1658 (2016)

    Article  Google Scholar 

  11. Lee, J.P.: Appl. Phys. Lett. 110, 071102 (2017)

    Article  ADS  Google Scholar 

  12. Streltsov, A., Adesso, G., Plenio, M.B.: Rev. Mod. Phys. 84, 041003 (2017)

    Article  ADS  Google Scholar 

  13. Lostaglio, M., Korzekwa, K., Jennings, D., et al.: Phys. Rev. X 5, 021001 (2015)

    Google Scholar 

  14. Marvian, I., Spekkens, R.W.: Phys. Rev. A 94, 052324 (2016)

    Article  ADS  Google Scholar 

  15. Chitambar, E., Hsieh, M.H.: Phys. Rev. Lett. 117, 020402 (2016)

    Article  ADS  Google Scholar 

  16. Chitambar, E., Gour, G.: Phys. Rev. Lett. 117, 030401 (2016)

    Article  ADS  Google Scholar 

  17. Winter, A., Yang, D.: Phys. Rev. Lett. 116, 120404 (2016)

    Article  ADS  Google Scholar 

  18. Zhou, Z.Q., Huelga, S.F., Li, C.F.: Phys. Rev. Lett. 115, 113002 (2015)

    Article  ADS  Google Scholar 

  19. Kiktenko, E.O., Fedorov, A.K., Strakhov, A.A.: Phys. Lett. A 379, 1409–1413 (2015)

    Article  ADS  Google Scholar 

  20. Borregaard, J., Sorensen, A.S., Cirac, J.I.: Phys. Rev. A 95, 042312 (2017)

    Article  ADS  Google Scholar 

  21. Mong, R.S.K., Clarke, D.J., Alicea, J.: Phys. Rev. X 4, 011036 (2014)

    Google Scholar 

  22. Lau, H.K., Plenio, M.B.: Phys. Rev. A 95, 022303 (2017)

    Article  ADS  Google Scholar 

  23. Xu, G.F., Zhang, J., Tong, D.M., et al.: Phys. Rev. Lett. 109, 170501 (2012)

    Article  ADS  Google Scholar 

  24. Loss, D., DiVincenzo, D.P.: Phys. Rev. A 57, 120 (1998)

    Article  ADS  Google Scholar 

  25. Papanastasiou, P., Ottaviani, C., Pirandola, S.: Phys.Rev. A 94, 042332 (2017)

    Article  ADS  Google Scholar 

  26. Zhang, W., Ding, D.S., Sheng, Y.B.: Phys. Rev. Lett. 118, 220501 (2017)

    Article  ADS  Google Scholar 

  27. Hu, J.Y., Yu, B., Jing, M.Y.: Light-Sci. Appl. 5, e16144 (2016)

    Article  Google Scholar 

  28. Shen, H.Z., Shao, X.Q., Wang, G.C.: Phys. Rev. E 93, 012107 (2016)

    Article  ADS  Google Scholar 

  29. Glauber, R.J.: Phys. Rev. 131, 2766 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  30. Kim, M.S., Son, W., Knight, P.L.: Phys. Rev. A 65, 032323 (2002)

    Article  ADS  Google Scholar 

  31. Vogel, W., Sperling, J.: Phys. Rev. A 89, 052302 (2014)

    Article  ADS  Google Scholar 

  32. Ma, Z., Wang, X.: Phys. Rev. A 75, 014304 (2007)

    Article  ADS  Google Scholar 

  33. Ye, M.Y., Sun, D., Zhang, Y.S.: Phys. Rev. A 70, 022326 (2004)

    Article  ADS  Google Scholar 

  34. Mani, A., Karimipour, V.: Phys. Rev. A 93, 032331 (2015)

    Article  ADS  Google Scholar 

  35. Bu, K., Kumar, A., Zhang, L.: Phys. Lett. A 381, 1670–1676 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  36. Wang, X., Sanders, B.C., Berry, D.W.: Phys. Rev. A 67, 042323 (2003)

    Article  ADS  Google Scholar 

  37. Peng, Y., Jiang, Y., Fan, H.: Phys. Rev. A 93, 032326 (2016)

    Article  ADS  Google Scholar 

  38. Singh, U., Bera, M.N., Dhar, H.S.: Phys. Rev. A 91, 052115 (2015)

    Article  ADS  Google Scholar 

  39. Zhang, Y.R., Shao, L.H., Li, Y.: Phys. Rev. A 93, 012334 (2016)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  41. Shao, L.H., Xi, Z., Fan, H., et al.: Phys. Rev. A 91, 042120 (2015)

    Article  ADS  Google Scholar 

  42. Mani, A., Karimipour, V.: Phys. Rev. A 92, 032331 (2015)

    Article  ADS  Google Scholar 

  43. Streltsov, A., Singh, U., Dhar, H.S.: Phys. Rev. Lett. 115, 020403 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  44. Yao, Y., Xiao, X., Ge, L., et al.: Phys. Rev. A 92, 022112 (2015)

    Article  ADS  Google Scholar 

  45. Shi, H.L., Liu, S.Y., Wang, X.H.: Phys. Rev. A95, 032307 (2017)

    Article  ADS  Google Scholar 

  46. Hu, M.L., Shen, S.Q., Fan, H.: Phys. Rev. A 96, 052309 (2017)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China, under Grant No. 11574041 and No. 11475037.

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Authors and Affiliations

  1. School of Physics, Dalian University of Technology, Dalian, 116024, China

    Ming-Song Ding, Ye-Xiong Zeng & Chong Li

  2. Information Science and Engineering College, Dalian Polytechnic University, Dalian, 116034, China

    Li Zheng

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  1. Ming-Song Ding
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  2. Li Zheng
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  3. Ye-Xiong Zeng
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  4. Chong Li
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All the authors were involved in the preparation of the manuscript. All the authors have read and approved the final manuscript.

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Correspondence to Chong Li.

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Ding, MS., Zheng, L., Zeng, YX. et al. Maximal Coherence in a Pre-Selected Basis. Int J Theor Phys 58, 1524–1533 (2019). https://doi.org/10.1007/s10773-019-04038-2

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  • DOI: https://doi.org/10.1007/s10773-019-04038-2

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