Skip to main content

Advertisement

Springer Nature Link
Log in

Quantum coherence and its distribution in the extended Ising chain

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

We investigate the two-spin coherence and its distribution in an extended Ising model with topological characterization. Some interesting discrepancies among the basis-dependent coherences under the different bases are found with the help of the three-spin interaction and magnetic field. The basis-independent coherence and its distribution (the collective and localized coherence) for the spin-pairs with different site distances are studied. We find that the collective coherence possesses the long-range property due to the contribution of classical correlation. We demonstrate that the first-order derivatives of the two-spin coherences can correctly characterize all of the topological quantum phase transitions regardless of the basis transformations, the site distances, or the types of coherence.

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
$34.99 /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 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

Explore related subjects

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

References

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

    MATH  Google Scholar 

  2. Vedral, V.: Introduction to Quantum Information Science. Oxford University Press, Oxford (2007)

    MATH  Google Scholar 

  3. Roßnagel, J., Abah, O., Schmidt-Kaler, F., Singer, K., Lutz, E.: Nanoscale heat engine beyond the carnot limit. Phys. Rev. Lett. 112, 030602 (2014)

    Article  ADS  Google Scholar 

  4. Lostaglio, M., Jennings, D., Rudolph, T.: Description of quantum coherence in thermodynamic processes requires constraints beyond free energy. Nat. Commun. 6, 6383 (2015)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  6. Lostaglio, M., Korzekwa, K., Jennings, D., Rudolph, T.: Quantum coherence, time-translation symmetry, and thermodynamics. Phys. Rev. X 5, 021001 (2015)

    Google Scholar 

  7. Giovannetti, V., Lloyd, S., Maccone, L.: Advances in quantum metrology. Nat. Photon. 5, 222 (2011)

    Article  ADS  Google Scholar 

  8. Li, C.M., Lambert, N., Chen, Y.N., Chen, G.Y., Nori, F.: Witnessing quantum coherence: from solid-state to biological systems. Sci. Rep. 2, 885 (2012)

    Article  Google Scholar 

  9. Engel, G.S., Calhoun, T.R., Read, E.L., Ahn, T.K., Manǎl, T., Cheng, Y.C., Blankenship, R.E., Fleming, G.R.: Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems. Nature 446, 782 (2007)

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  11. Huelga, S.F., Plenio, M.B.: Vibrations, quanta and biology. Contemp. Phys. 54, 181 (2013)

    Article  ADS  Google Scholar 

  12. Romero, E., Augulis, R., Novoderezhkin, V.I., Ferretti, M., Thieme, J., Zigmantas, D., van Grondelle, R.: Quantum coherence in photosynthesis for efficient solar-energy conversion. Nat. Phys. 10, 677 (2014)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  14. 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 

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

    Article  ADS  Google Scholar 

  16. Ma, J.J., Yadin, B., Girolami, D., Vedral, V., Gu, M.: Converting coherence to quantum correlations. Phys. Rev. Lett. 116, 160407 (2016)

    Article  ADS  Google Scholar 

  17. Hu, M.L., Fan, H.: Evolution equation for quantum coherence. Sci. Rep. 6, 29260 (2016)

    Article  ADS  Google Scholar 

  18. Yadin, B., Vedral, V.: General framework for quantum macroscopicity in terms of coherence. Phys. Rev. A 93, 022122 (2016)

    Article  ADS  Google Scholar 

  19. Pozzobom, M.B., Maziero, J.: Environment-induced quantum coherence spreading of a qubit. Ann. Phys. 377, 243 (2017)

    Article  MATH  ADS  Google Scholar 

  20. Wu, W., Xu, J.B.: Quantum coherence of spin-boson model at finite temperature. Ann. Phys. 377, 48 (2017)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  22. 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 

  23. 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 

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

    Article  MathSciNet  ADS  Google Scholar 

  25. Yu, X.D., Zhang, D.J., Liu, C.L., Tong, D.M.: Measure-independent freezing of quantum coherence. Phys. Rev. A 93, 060303(R) (2016)

    Article  ADS  Google Scholar 

  26. Yu, C.S.: Quantum coherence via skew information and its polygamy. Phys. Rev. A 95, 042337 (2017)

    Article  ADS  Google Scholar 

  27. Radhakrishnan, C., Parthasarathy, M., Jambulingam, S., Byrnes, T.: Distribution of quantum coherence in multipartite systems. Phys. Rev. Lett. 116, 150504 (2016)

    Article  ADS  Google Scholar 

  28. Li, S.P., Sun, Z.H.: Local and intrinsic quantum coherence in critical systems. Phys. Rev. A 98, 022317 (2018)

    Article  ADS  Google Scholar 

  29. Radhakrishnan, C., Ding, Z., Shi, F.Z., Du, J.F., Byrnes, T.: Basis-independent quantum coherence and its distribution. Ann. Phys. 409, 167906 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  30. Streltsov, A., Chitambar, E., Rana, S., Bera, M.N., Winter, A., Lewenstein, M.: Entanglement and coherence in quantum state merging. Phys. Rev. Lett. 116, 240405 (2016)

    Article  ADS  Google Scholar 

  31. Shi, H.L., Liu, S.Y., Wang, X.H., Yang, W.L., Yang, Z.Y., Fan, H.: Coherence depletion in the Grover quantum search algorithm. Phys. Rev. A 95, 032307 (2017)

    Article  MathSciNet  ADS  Google Scholar 

  32. Karpat, G., Cakmak, B., Fanchini, F.F.: Quantum coherence and uncertainty in the anisotropic XY chain. Phys. Rev. B 90, 104431 (2014)

    Article  ADS  Google Scholar 

  33. Cheng, W.W., Du, Z.Z., Gong, L.Y., Zhao, S.M., Liu, J.M.: Signature of topological quantum phase transitions via Wigner–Yanase skew information. Europhys. Lett. 108, 46003 (2014)

    Article  ADS  Google Scholar 

  34. Cakmak, B., Karpat, G., Fanchini, F.F.: Factorization and criticality in the anisotropic XY chain via correlations. Entropy 17, 790 (2015)

    Article  ADS  Google Scholar 

  35. Cheng, W.W., Li, J.X., Shan, C.J., Gong, L.Y., Zhao, S.M.: Criticality, factorization and Wigner–Yanase skew information in quantum spin chains. Quantum Inf. Process. 14, 2535 (2015)

    Article  MATH  ADS  Google Scholar 

  36. Malvezzi, A.L., Karpat, G., Cakmak, B., Fanchini, F.F., Debarba, T., Vianna, R.O.: Quantum correlations and coherence in spin-1 Heisenberg chains. Phys. Rev. B 93, 184428 (2016)

    Article  ADS  Google Scholar 

  37. Li, Y.C., Lin, H.Q.: Quantum coherence and quantum phase transitions. Sci. Rep. 6, 26365 (2016)

    Article  ADS  Google Scholar 

  38. Lei, S.G., Tong, P.Q.: Wigner–Yanase skew information and quantum phase transition in one-dimensional quantum spin-1/2 chains. Quantum Inf. Process. 15, 1811 (2016)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  39. Radhakrishnan, C., Ermakov, I., Byrnes, T.: Quantum coherence of planar spin models with Dzyaloshinsky–Moriya interaction. Phys. Rev. A 96, 012341 (2017)

    Article  ADS  Google Scholar 

  40. Radhakrishnan, C., Parthasarathy, M., Jambulingam, S., Byrnes, T.: Quantum coherence of the Heisenberg spin models with Dzyaloshinsky–Moriya interactions. Sci. Rep. 7, 13865 (2017)

    Article  ADS  Google Scholar 

  41. Sha, Y.T., Wang, Y., Sun, Z.H., Hou, X.W.: Thermal quantum coherence and correlation in the extended XY spin chain. Ann. Phys. 392, 229–241 (2018)

    Article  MathSciNet  ADS  Google Scholar 

  42. Yin, S.Y., Song, J., Xu, X.X., Zhang, Y.J., Liu, S.T.: Quantum coherence dynamics of three-qubit states in XY spin-chain environment. Quantum Inf. Process. 17, 296 (2018)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  43. Hu, M.L., Gao, Y.Y., Fan, H.: Steered quantum coherence as a signature of quantum phase transitions in spin chains. Phys. Rev. A 101, 032305 (2020)

    Article  MathSciNet  ADS  Google Scholar 

  44. Yin, S.Y., Song, J., Liu, S.T., Song, G.L.: Quantum coherence and topological quantum phase transitions in the extended XY chain. Phys. Lett. A 389, 127089 (2021)

    Article  MathSciNet  Google Scholar 

  45. Liu, B.Q., Shao, B., Li, J.G., Zou, J., Wu, L.A.: Quantum and classical correlations in the one-dimensional XY model with Dzyaloshinskii–Moriya interaction. Phys. Rev. A 83, 052112 (2011)

    Article  ADS  Google Scholar 

  46. Ye, B.L., Li, B., Wang, Z.X., Li-Jost, X.Q., Fei, S.M.: Quantum Fisher information and coherence in one-dimensional XY spin models with Dzyaloshinsky–Moriya interactions. Sci. China Phys. Mech. Astron. 61, 110312 (2018)

    Article  ADS  Google Scholar 

  47. Yi, T.C., You, W.L., Wu, N., Oles, A.M.: Criticality and factorization in the Heisenberg chain with Dzyaloshinskii–Moriya interaction. Phys. Rev. B 100, 024423 (2019)

    Article  ADS  Google Scholar 

  48. Wang, C.X., Chen, L., Han, R.S., Zhang, Y.Q.: Quantum steering and quantum coherence in XY model with Dzyaloshinskii–Moriya interaction. Quantum Inf. Process. 19, 330 (2020)

    Article  MathSciNet  ADS  Google Scholar 

  49. Vedral, V., Plenio, M.B., Rippin, M.A., Knight, P.L.: Quantifying entanglement. Phys. Rev. Lett. 78, 2275 (1997)

    Article  MathSciNet  MATH  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  51. Hu, M.L., Shen, S.Q., Fan, H.: Maximum coherence in the optimal basis. Phys. Rev. A 96, 052309 (2017)

    Article  ADS  Google Scholar 

  52. Luo, S.L., Sun, Y.: Quantum coherence versus quantum uncertainty. Phys. Rev. A 96, 022130 (2017)

    Article  MathSciNet  ADS  Google Scholar 

  53. Singh, U., Bera, M.N., Dhar, H.S., Pati, A.K.: Maximally coherent mixed states: complementarity between maximal coherence and mixedness. Phys. Rev. A 91, 052115 (2015)

    Article  ADS  Google Scholar 

  54. Yao, Y., Dong, G.H., Xiao, X., Sun, C.P.: Frobenius-norm-based measures of quantum coherence and asymmetry. Sci. Rep. 6, 32010 (2016)

    Article  ADS  Google Scholar 

  55. Zhang, J., Yang, S.R., Zhang, Y., Yu, C.S.: The classical correlation limits the ability of the measurement-induced average coherence. Sci. Rep. 7, 45598 (2017)

    Article  ADS  Google Scholar 

  56. Radhakrishnan, C., lü, Z.G., Jing, J., Byrnes, T.: Dynamics of quantum coherence in a spin-star system: bipartite initial state and coherence distribution. Phys. Rev. A 100, 042333 (2019)

  57. Cao, H., Radhakrishnan, C., Su, M., Ali, M.M., Zhang, C., Huang, Y.F., Byrnes, T., Li, C.F., Guo, G.C.: Fragility of quantum correlations and coherence in a multipartite photonic system. Phys. Rev. A 102, 012403 (2020)

    Article  ADS  Google Scholar 

  58. Qin, M.: Renormalization of quantum coherence and quantum phase transition in the Ising model. Physica A 561, 125176 (2021)

    Article  MathSciNet  Google Scholar 

  59. Zeng, B., Chen, X., Zhou, D.L., Wen, X.G.: Quantum Information Meets Quantum Matter: From Quantum Entanglement to Topological Phases of Many-Body Systems. Springer, New York (2019)

    Book  MATH  Google Scholar 

  60. Theurer, T., Egloff, D., Zhang, L., Martin, B.P.: Quantifying operations with an application to coherence. Phys. Rev. Lett. 122, 190405 (2019)

    Article  ADS  Google Scholar 

  61. Oszmaniec, M., Biswas, T.: Operational relevance of resource theories of quantum measurements. Quantum 3, 133 (2019)

    Article  Google Scholar 

  62. Baek, K., Sohbi, A., Lee, J., Kim, J., Nha, H.: Quantifying coherence of quantum measurements. New J. Phys. 22, 093019 (2019)

    Article  MathSciNet  Google Scholar 

  63. Zhang, G., Song, Z.: Topological characterization of extended quantum Ising models. Phys. Rev. Lett. 115, 177204 (2015)

    Article  ADS  Google Scholar 

  64. Yin, S.Y., Song, J., Zhang, Y.J., Liu, S.T.: Quantum Fisher information in quantum critical systems with topological characterization. Phys. Rev. B 100, 184417 (2019)

    Article  ADS  Google Scholar 

  65. Zhang, Y.R., Zeng, Y., Fan, H., You, J.Q., Nori, F.: Characterization of topological states via dual multipartite entanglement. Phys. Rev. Lett. 120, 250501 (2018)

    Article  MathSciNet  ADS  Google Scholar 

  66. Wang, Y.K., Zhang, Y.R., Fan, H.: One-way deficit and quantum phase transitions in XY model and extended Ising model. Quantum Inf. Process. 18, 19 (2019)

    Article  MATH  ADS  Google Scholar 

  67. Zhang, X.Z., Guo, J.L.: Quantum correlation and quantum phase transition in the one-dimensional extended Ising model. Quantum Inf. Process. 16, 223 (2017)

    Article  MathSciNet  MATH  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China under the Grant Nos. 61575055, 11874132, and 11675046. We thank Dr. Biao-Liang Ye for helpful suggestions.

Author information

Authors and Affiliations

  1. Key Laboratory for Photonic and Electronic Bandgap Materials, Ministry of Education, School of Physics and Electronic Engineering, Harbin Normal University, Harbin, 150025, China

    Shaoying Yin, Yueyuan Wang, Lin Li & Wenjun Sun

  2. School of Physics, Harbin Institute of Technology, Harbin, 150001, China

    Jie Song & Shutian Liu

Authors
  1. Shaoying Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jie Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yueyuan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Lin Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Wenjun Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Shutian Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shutian Liu.

Additional information

Publisher's Note

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

Appendix: TQPTs driven by the magnetic field

Appendix: TQPTs driven by the magnetic field

In this Appendix, by means of the energy spectra of the ground state, winding parameter, and characteristic equations, we analyze the topological characterization of the extended Ising model as the magnetic field is the driving parameter. Then, we consider the parameters of the extended Ising model as \(N=201\), \(\gamma =1\), \(\delta = 1\), and \(\alpha =1.5\). The critical points of TQPTs can be derived from the characteristic equation \(1.5\xi ^2 + \xi -\lambda = 0\), where \(\xi = \exp \left( \frac{i2\pi k}{N}\right) \) and \(|\xi | = 1\), and it can be numerically verified that \(\lambda _{c1}=-1.5\), \(\lambda _{c2}=0.5\), and \(\lambda _{c3}=2.5\) satisfy the characteristic equation [28, 64,65,66]. The energy spectra as a function of \(\lambda \) are shown in Fig. 6a, which also manifest the locations of the critical point again. Moreover, the trajectories of winding vectors are plotted in Fig. 6b with \(\lambda =-2, -1, 2\), and 3. The winding numbers can be obtained in the auxiliary \(y-z\) plane according to Eq. (17), and it changes from 0 to 2 at \(\lambda _{c1}=-1.5\), from 2 to 1 at \(\lambda _{c2}=0.5\), and from 1 to 0 at \(\lambda _{c3}=2.5\).

Fig. 6
figure 6

a Energy spectra as a function of \(\lambda \). b Trajectories of winding vectors in y–z plane with parameters \(\lambda =-2, -1, 2\), and 3, the winding numbers are 0, 2, 1, and 0, respectively. The other parameters are set to \(N=201\), \(\gamma =1\), \(\delta =1\), and \(\alpha = 1.5\)

Full size image

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yin, S., Song, J., Wang, Y. et al. Quantum coherence and its distribution in the extended Ising chain. Quantum Inf Process 20, 326 (2021). https://doi.org/10.1007/s11128-021-03266-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-021-03266-y

Keywords

Search

Navigation