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Transformations of multilevel coherent states under coherence-preserving operations

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Abstract

Quantum coherence, emerging from the “superposition” of quantum states, is widely used in various information processing tasks. Recently, the resource theory of multilevel quantum coherence is attracting substantial attention. In this paper, we mainly study the transformations of resource pure states via free operations in the theoretical framework for multilevel coherence. We prove that any two multilevel coherent resource pure states can be interconverted with a nonzero probability via a completely positive and trace non-increasing k-coherence-preserving map. Meanwhile, we present the condition of the interconversions of two multilevel coherent resource pure states under k-coherence-preserving operations. In addition, we obtain that in the resource-theoretic framework of multilevel coherence, no resource state is isolated, that is, given a multilevel coherent pure state ∣ψ〉, there exists another multilevel coherent pure state ∣ϕ〉 and a k-coherence-preserving operation Λk, such that Λk(∣ϕ〉) = ∣ψ〉.

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References

  1. T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014), arXiv: 1311.0275.

    Article  ADS  Google Scholar 

  2. A. Streltsov, G. Adesso, and M. B. Plenio, Rev. Mod. Phys. 89, 041003 (2017), arXiv: 1609.02439.

    Article  ADS  Google Scholar 

  3. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002), arXiv: quant-ph/0101098.

    Article  ADS  Google Scholar 

  4. V. Giovannetti, S. Lloyd, and L. Maccone, Nat. Photon. 5, 222 (2011), arXiv: 1102.2318.

    Article  ADS  Google Scholar 

  5. G. Tóth, and I. Apellaniz, J. Phys. A-Math. Theor. 47, 424006 (2014), arXiv: 1405.4878.

    Article  ADS  Google Scholar 

  6. M. Lostaglio, D. Jennings, and T. Rudolph, Nat. Commun. 6, 6383 (2015), arXiv: 1405.2188.

    Article  ADS  Google Scholar 

  7. V. Narasimhachar, and G. Gour, Nat. Commun. 6, 7689 (2015), arXiv: 1409.7740.

    Article  ADS  Google Scholar 

  8. S. Lloyd, J. Phys.-Conf. Ser. 302, 012037 (2011).

    Article  Google Scholar 

  9. A. Winter, and D. Yang, Phys. Rev. Lett. 116, 120404 (2016), arXiv: 1506.07975.

    Article  ADS  Google Scholar 

  10. M. L. Hu, X. Hu, J. Wang, Y. Peng, Y. R. Zhang, and H. Fan, Phys. Rep. 762–764, 1 (2018), arXiv: 1703.01852.

    ADS  Google Scholar 

  11. F. Bischof, H. Kampermann, and D. Bruß, Phys. Rev. Lett. 123, 110402 (2019), arXiv: 1812.00018.

    Article  ADS  MathSciNet  Google Scholar 

  12. E. Chitambar, and G. Gour, Rev. Mod. Phys. 91, 025001 (2019), arXiv: 1806.06107.

    Article  ADS  Google Scholar 

  13. X. D. Yu, D. J. Zhang, G. F. Xu, and D. M. Tong, Phys. Rev. A 94, 060302 (2016), arXiv: 1606.03181.

    Article  ADS  Google Scholar 

  14. M. L. Hu, and H. Fan, Sci. China-Phys. Mech. Astron. 63, 230322 (2020), arXiv: 1812.04385.

    Article  ADS  Google Scholar 

  15. M. J. Zhao, T. Ma, and Y. Q. Ma, Sci. China-Phys. Mech. Astron. 61, 020311 (2018), arXiv: 1712.09769.

    Article  ADS  Google Scholar 

  16. M. B. Plenio, and S. Virmani, Quantum Inform. Comput. 7, 1 (2007).

    Article  Google Scholar 

  17. R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Rev. Mod. Phys. 81, 865 (2009), arXiv: quant-ph/0702225.

    Article  ADS  Google Scholar 

  18. O. Gühne, and G. Tóth, Phys. Rep. 474, 1 (2009), arXiv: 0811.2803.

    Article  ADS  MathSciNet  Google Scholar 

  19. E. Chitambar, and G. Gour, Phys. Rev. Lett. 117, 030401 (2016).

    Article  ADS  Google Scholar 

  20. B. Yadin, J. Ma, D. Girolami, M. Gu, and V. Vedral, Phys. Rev. X 6, 041028 (2016), arXiv: 1512.02085.

    Google Scholar 

  21. Y. Peng, Y. Jiang, and H. Fan, Phys. Rev. A 93, 032326 (2016), arXiv: 1511.02576.

    Article  ADS  Google Scholar 

  22. J. Åberg, arXiv: quant-ph/0612146.

  23. F. Levi, and F. Mintert, New J. Phys. 16, 033007 (2014), arXiv: 1310.6962.

    Article  ADS  Google Scholar 

  24. J. Sperling, and W. Vogel, Phys. Scr. 90, 074024 (2015).

    Article  ADS  Google Scholar 

  25. N. Killoran, F. E. S. Steinhoff, and M. B. Plenio, Phys. Rev. Lett. 116, 080402 (2016), arXiv: 1505.07393.

    Article  ADS  Google Scholar 

  26. G. D. Scholes, G. R. Fleming, L. X. Chen, A. Aspuru-Guzik, A. Buchleitner, D. F. Coker, G. S. Engel, R. van Grondelle, A. Ishizaki, D. M. Jonas, J. S. Lundeen, J. K. McCusker, S. Mukamel, J. P. Ogilvie, A. Olaya-Castro, M. A. Ratner, F. C. Spano, K. B. Whaley, and X. Zhu, Nature 543, 647 (2017).

    Article  ADS  Google Scholar 

  27. M. Ringbauer, T. R. Bromley, M. Cianciaruso, L. Lami, W. Y. S. Lau, G. Adesso, A. G. White, A. Fedrizzi, and M. Piani, Phys. Rev. X 8, 041007 (2018), arXiv: 1707.05282.

    Google Scholar 

  28. F. G. S. L. Brandão, and M. B. Plenio, Nat. Phys. 4, 873 (2008).

    Article  Google Scholar 

  29. M. A. Nielsen, Phys. Rev. Lett. 83, 436 (1999), arXiv: quant-ph/9811053.

    Article  ADS  Google Scholar 

  30. G. Vidal, Phys. Rev. Lett. 83, 1046 (1999), arXiv: quant-ph/9902033.

    Article  ADS  Google Scholar 

  31. S. Du, Z. Bai, and Y. Guo, Phys. Rev. A 91, 052120 (2015), arXiv: 1503.09176

    Article  ADS  Google Scholar 

  32. S. Du, Z. Bai, and Y. Guo, Phys. Rev. A 95, 029901 (2017).

    Article  ADS  Google Scholar 

  33. S. Du, Z. Bai, and X. Qi, Quantum Inform. Comput. 15, 1307 (2015).

    Article  Google Scholar 

  34. M. Hebenstreit, C. Spee, and B. Kraus, Phys. Rev. A 93, 012339 (2016).

    Article  ADS  Google Scholar 

  35. D. Sauerwein, N. R. Wallach, G. Gour, and B. Kraus, Phys. Rev. X 8, 031020 (2018), arXiv: 1711.11056.

    Google Scholar 

  36. P. Contreras-Tejada, C. Palazuelos, and J. I. de Vicente, Phys. Rev. Lett. 122, 120503 (2019), arXiv: 1807.11395.

    Article  ADS  Google Scholar 

  37. E. Chitambar, and G. Gour, Phys. Rev. A 94, 052336 (2016), arXiv: 1602.06969

    Article  ADS  Google Scholar 

  38. E. Chitambar, and G. Gour, Phys. Rev. A 95, 019902 (2017).

    Article  ADS  Google Scholar 

  39. H. L. Shi, X. H. Wang, S. Y. Liu, W. L. Yang, Z. Y. Yang, and H. Fan, Sci. Rep. 7, 14806 (2017).

    Article  ADS  Google Scholar 

  40. G. Torun, and A. Yildiz, Phys. Rev. A 97, 052331 (2018), arXiv: 1805.06489.

    Article  ADS  Google Scholar 

  41. I. Marvian, and R. W. Spekkens, Phys. Rev. A 94, 052324 (2016), arXiv: 1602.08049.

    Article  ADS  Google Scholar 

  42. S. Chin, Phys. Rev. A 96, 042336 (2017), arXiv: 1702.03219.

    Article  ADS  Google Scholar 

  43. N. Johnston, C. K. Li, S. Plosker, Y. T. Poon, and B. Regula, Phys. Rev. A 98, 022328 (2018), arXiv: 1806.00653.

    Article  ADS  Google Scholar 

  44. B. Regula, M. Piani, M. Cianciaruso, T. R. Bromley, A. Streltsov, and G. Adesso, New J. Phys. 20, 033012 (2018), arXiv: 1704.04153.

    Article  ADS  Google Scholar 

  45. E. Chitambar, J. I. de Vicente, M. W. Girard, and G. Gour, arXiv: quant-ph/1711.03835.

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Authors and Affiliations

  1. School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, 050024, China

    LiMei Zhang & Ting Gao

  2. Department of Mathematics and Computer Science, Hengshui University, Hengshui, 053000, China

    LiMei Zhang

  3. College of Physics, Hebei Key Laboratory of Photophysics Research and Application, Hebei Normal University, Shijiazhuang, 050024, China

    FengLi Yan

Authors
  1. LiMei Zhang
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  2. Ting Gao
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  3. FengLi Yan
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Corresponding authors

Correspondence to Ting Gao or FengLi Yan.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant No. 12071110), the Hebei Natural Science Foundation of China (Grant Nos. A2020205014, and A2018205125), and the Science and Technology Project of Hebei Education Department (Grant Nos. ZD2020167, and ZD2021066).

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Zhang, L., Gao, T. & Yan, F. Transformations of multilevel coherent states under coherence-preserving operations. Sci. China Phys. Mech. Astron. 64, 260312 (2021). https://doi.org/10.1007/s11433-021-1696-y

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  • DOI: https://doi.org/10.1007/s11433-021-1696-y

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