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Quantum coherence dynamics of three-qubit states in XY spin-chain environment

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Abstract

We investigate the dynamics of quantum coherence, based on relative entropy and quantum skew information, for tripartite systems in a quantum-critical environment. We demonstrate that initial states, the strength of magnetic field, anisotropy parameter, system–environment coupling, and the scale of the environment strongly affect coherence evolution. We find that two measures of coherence are frozen for the initial W state coupled to an XY spin-chain environment as the system–environment coupling satisfies certain conditions. We compare the dynamics of quantum coherence with that of the entanglement and the quantum discord. The analysis shows no hierarchical relationship among them.

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References

  1. Bennett, C.H., DiVincenzo, D.P.: Quantum information and computation. Nature 404, 247 (2000)

    Article  ADS  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.: Introduction to Quantum Information Science. Oxford University Press, Oxford (2007)

    MATH  Google Scholar 

  4. Streltsov, A., Adesso, G., Plenio, M.B.: Colloquium: Quantum coherence as a resource. Rev. Mod. Phys. 89, 041003 (2017)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  6. 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 

  7. 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 

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

    Article  ADS  Google Scholar 

  9. 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 

  10. Engel, G.S., Calhoun, T.R., Read, E.L., Ahn, T.K., Mančal, 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 

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

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  13. 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, 676 (2014)

    Article  Google Scholar 

  14. Åberg, J.: Quantifying Superposition. arXiv:quant-ph/0612146vl

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. 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 

  18. 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 

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

    Article  ADS  Google Scholar 

  20. 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 

  21. Yao, Y., Xiao, X., Ge, L., Sun, C.P.: Quantum coherence in multipartite systems. Phys. Rev. A 92, 022112 (2015)

    Article  ADS  Google Scholar 

  22. 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 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  25. 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 

  26. 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 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Google Scholar 

  30. Lostaglio, M., Korzekwa, K., Milne, A.: Markovian evolution of quantum coherence under symmetric dynamics. Phys. Rev. A 96, 032109 (2017)

    Article  ADS  Google Scholar 

  31. Yuan, Z.G., Zhang, P., Li, S.S.: Disentanglement of two qubits coupled to an XY spin chain: role of quantum phase transition. Phys. Rev. A 76, 042118 (2007)

    Article  ADS  Google Scholar 

  32. Liu, B.Q., Shao, B., Zou, J.: Quantum discord for a central two-qubit system coupled to an XY- spin-chain environment. Phys. Rev. A 82, 062119 (2010)

    Article  ADS  Google Scholar 

  33. Ma, X.S., Wang, A.M., Cao, Y.: Entanglement evolution of three-qubit states in a quantum-critical environment. Phys. Rev. B 76, 155327 (2007)

    Article  ADS  Google Scholar 

  34. Guo, J.L., Long, G.L.: Quantum correlation dynamics of a three-qubit system coupled to an XY spin chain. Eur. Phys. J. D 67, 53 (2013)

    Article  ADS  Google Scholar 

  35. Yin, S.Y., Liu, Q.X., Song, J., Xu, X.X., Zhou, K.Y., Liu, S.T.: Quantum correlations dynamics of a three-qubit system coupled to an XY spin chain: role of coupling strengths. Chin. Phys. B 26, 100501 (2017)

    Article  ADS  Google Scholar 

  36. Gross, C., Bloch, I.: Quantum simulations with ultracold atoms in optical lattices. Science 357, 995–1001 (2017)

    Article  ADS  Google Scholar 

  37. Simon, J., Bakr, W.S., Ma, R., Tai, M.E., Preiss, P.M., Greiner, M.: Quantum simulation of antiferromagnetic spin chains in an optical lattice. Nature 472, 307–312 (2011)

    Article  ADS  Google Scholar 

  38. Dai, H.N., Yang, B., Reingruber, A., Xu, X.F., Jiang, X., Chen, Y.A., Yuan, Z.S., Pan, J.-W.: Generation and detection of atomic spin entanglement in optical lattices. Nat. Phys. 12, 783–787 (2016)

    Article  Google Scholar 

  39. Yang, B., Dai, H.N., Sun, H., Reingruber, A., Yuan, Z.S., Pan, J.-W.: Spin-dependent optical superlattice. Phys. Rev. A 96, 011602(R) (2017)

    Article  ADS  Google Scholar 

  40. Ma, X.S., Cong, H.S., Zhang, J.Y., Wang, A.M.: Entanglement dynamics of three-qubit states under an XY spin-chain environment. Eur. Phys. J. D 48, 285 (2008)

    Article  ADS  Google Scholar 

  41. Cheng, W.W., Shan, C.J., Huang, Y.X., Liu, T.K., Li, H.: Entanglement dynamics from quantum critical environment: role of Dzyaloshinsky–Moriya interaction. Physica E 42, 1544 (2010)

    Article  ADS  Google Scholar 

  42. 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 

  43. 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 

  44. Wang, L., Yang, C.H., Wang, J.F., Lei, S.G.: The size effect of the quantum coherence in the transverse-field XY chain. Physica B 503, 121 (2016)

    Article  ADS  Google Scholar 

  45. 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 

  46. 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  ADS  Google Scholar 

  47. 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 

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

    Article  ADS  Google Scholar 

  49. 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  ADS  MathSciNet  Google Scholar 

  50. Huang, Z.M., Situ, H.Z., Zhang, C.: Quantum coherence and correlation in spin models with Dzyaloshinskii–Moriya interaction. Int. J. Theor. Phys. 56, 2178 (2017)

    Article  MathSciNet  Google Scholar 

  51. 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 

  52. Hui, N.J., Xu, Y.Y., Wang, J.C., Zhang, Y.X., Hu, Z.D.: Quantum coherence and quantum phase transition in the XY model with staggered Dzyaloshinsky–Moriya interaction. Physica B 510, 7 (2017)

    Article  ADS  Google Scholar 

  53. 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 

  54. Li, M., Fei, S.M., Wang, Z.X.: A lower bound of concurrence for multipartite quantum states. J. Phys. A Math. Theor. 42, 145303 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  55. Rulli, C.C., Sarandy, M.S.: Global quantum discord in multipartite systems. Phys. Rev. A 84, 042109 (2011)

    Article  ADS  Google Scholar 

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Acknowledgements

This work was supported by National Basic Research Program of China (Grant No. 2013CBA01702), National Natural Science Foundation of China (Grant Nos. 61575055, 61377016, 10974039, 61307072, 61308017, and 61405056), and Special Fund Project of Harbin Science and Technology Innovation Talents Research (RC2017QN017004).

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Authors and Affiliations

  1. Department of Physics, Harbin Institute of Technology, Harbin, 150001, China

    Shaoying Yin, Jie Song, Xuexin Xu & Shutian Liu

  2. Department of Physics, Harbin University, Harbin, 150086, China

    Shaoying Yin & Yujun Zhang

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  1. Shaoying Yin
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Correspondence to Shutian Liu.

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Yin, S., Song, J., Xu, X. et al. Quantum coherence dynamics of three-qubit states in XY spin-chain environment. Quantum Inf Process 17, 296 (2018). https://doi.org/10.1007/s11128-018-2066-8

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