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Dynamics of quantum coherence in two-dimensional quantum walk on finite lattices

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Abstract.

We study the dynamics of the l1 norm coherence in a two-dimensional quantum walk on finite lattices with four-dimensional (4D) and two-dimensional (2D) coins. It is observed that the boundaries suppress the growth of coherence of both the whole system and the position subsystem. The coherence of the quantum walk with a 2D coin is larger than that of the quantum walk with a 4D coin when it stabilizes after a number of steps. We also analyze the influence of two kinds of noise, i.e., broken links and lattice congestion, on the coherence of a bounded quantum walk. Experimental results show that both the broken links and the lattice congestion with low probability slightly increase the coherence of the whole system and the position subsystem. However, a high noise level significantly suppresses the growth of coherence, especially for static noise. The coherence of the coin subsystem is also analyzed and we find that the boundaries result in a large fluctuation of coherence of the coin subsystem.

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References

  1. M.N. Barber, B.W. Ninham, Random and Restricted Walks: Theory and Applications (Gordon and Breach, New York, 1970)

  2. J. Kempe, Contemp. Phys. 44, 307 (2003)

    Article  ADS  Google Scholar 

  3. A. Romanelli, R. Siri, G. Abal, A. Auyuanet, R. Donangelo, Physica A 347, 137 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  4. A.C. Oliveira, R. Portugal, R. Donangelo, Phys. Rev. A 74, 012312 (2006)

    Article  ADS  Google Scholar 

  5. A.C. Oliveira, R. Portugal, R. Donangelo, Two-dimensional quantum walks with boundaries, in Proceedings of 1st WECIQ, Pelotas, Brazil (UCPel, 2006) pp. 211--218

  6. C. Di Franco, M. Mc Gettrick, T. Busch, Phys. Rev. Lett. 106, 080502 (2011)

    Article  ADS  Google Scholar 

  7. P. Xue, R. Zhang, Z.H. Bian, X. Zhan, H. Qin, B.C. Sanders, Phys. Rev. A 92, 042316 (2015)

    Article  ADS  Google Scholar 

  8. B. Kollar, J. Novotny, T. Kiss, I. Jex, Eur. Phys. J. Plus 129, 103 (2014)

    Article  Google Scholar 

  9. Y.C. Zhang, W.S. Bao, X. Wang, X.Q. Fu, Chin. Phys. B 24, 080307 (2015)

    Article  ADS  Google Scholar 

  10. D. Li, M. Mc Gettrick, W.W. Zhang, K.J. Zhang, Int. J. Theor. Phys. 54, 2771 (2015)

    Article  Google Scholar 

  11. J. Zhao, P.Q. Tong, Quantum Inf. Process. 14, 2357 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  12. K.R. Motes, A. Gilchrist, P.P. Rohde, Sci. Rep. 6, 19864 (2016)

    Article  ADS  Google Scholar 

  13. T. Chen, X.D. Zhang, Sci. Rep. 6, 25767 (2016)

    Article  ADS  Google Scholar 

  14. Y.Z. Xu, G.D. Guo, S. Lin, Int. J. Theor. Phys. 55, 4060 (2016)

    Article  Google Scholar 

  15. C.S. Wang, X.J. Ye, Quantum Inf. Process. 15, 1897 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  16. A. Childs, R. Cleve, E. Deotto, E. Farhi, S. Gutmann, D. Spielman, Exponential algorithmic speedup by quantum walk, in Proceedings of the thirty-fifth annual ACM symposium on Theory of computing (ACM, 2003) p. 59

  17. N. Shenvi, J. Kempe, K.B. Whaley, Phys. Rev. A 67, 052307 (2003)

    Article  ADS  Google Scholar 

  18. V. Potocek, A. Gabris, T. Kiss, I. Jex, Phys. Rev. A 79, 012325 (2009)

    Article  ADS  Google Scholar 

  19. Y.M. Liu, H.W. Chen, Z.H. Liu, X.L. Xue, W.N. Zhu, Acta Phys. Sin. 64, 010301 (2015)

    Google Scholar 

  20. X.L. Xue, H.W. Chen, Z.H. Liu, B.B. Zhang, Acta Phys. Sin. 65, 080302 (2016)

    Google Scholar 

  21. X.L. Xue, H.W. Chen, Z.H. Liu, Int. J. Quantum Inf. 14, 1650035 (2016)

    Article  Google Scholar 

  22. A. Streltsov, G. Adesso, M.B. Plenio, arXiv:1609.02439 (2016)

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

    Article  ADS  Google Scholar 

  24. Y. Yao, X. Xiao, L. Ge, C.P. Sun, Phys. Rev. A 92, 022112 (2015)

    Article  ADS  Google Scholar 

  25. Y. Yao, G.H. Dong, X. Xiao, C.P. Sun, Sci. Rep. 6, 32010 (2016)

    Article  ADS  Google Scholar 

  26. J.C. Wang, Z.H. Tian, J.L. Jing, H. Fan, Phys. Rev. A 93, 062105 (2016)

    Article  ADS  Google Scholar 

  27. X.B. Liu, Z.H. Tian, J.C. Wang, J.L. Jing, Ann. Phys. 366, 102 (2016)

    Article  ADS  Google Scholar 

  28. X.Y. Hu, Phys. Rev. A 94, 012326 (2016)

    Article  ADS  Google Scholar 

  29. M.M. Chen, Y. Luo, L.H. Shao, Y.M. Li, arXiv:1612.05355 (2016)

  30. Y.N. Guo, K. Zeng, Q.L. Tian, Z.D. Li, arXiv:1612.08791 (2016)

  31. M.L. Hu, H. Fan, Sci. Rep. 6, 29260 (2016)

    Article  ADS  Google Scholar 

  32. H.Z. Situ, X.Y. Hu, Quantum Inf. Process. 15, 4649 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  33. Z.M. Huang, H.Z. Situ, Ann. Phys. 377, 484 (2017)

    Article  ADS  Google Scholar 

  34. Z.M. Huang, H.Z. Situ, Int. J. Theor. Phys. 56, 503 (2017)

    Article  Google Scholar 

  35. M. Hillery, Phys. Rev. A 93, 012111 (2016)

    Article  ADS  Google Scholar 

  36. J.J. Ma, B. Yadin, D. Girolami, V. Vedral, M. Gu, Phys. Rev. Lett. 116, 160407 (2016)

    Article  ADS  Google Scholar 

  37. J.M. Matera, D. Egloff, N. Killoran, M.B. Plenio, Quantum Sci. Technol. 1, 01LT01 (2016)

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Electronic and Information Engineering, Foshan University, 528000, Foshan, China

    Zhimin He

  2. School of Economics and Management, Wuyi University, 529020, Jiangmen, China

    Zhiming Huang

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

    Haozhen Situ

Authors
  1. Zhimin He
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  2. Zhiming Huang
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  3. Haozhen Situ
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Correspondence to Haozhen Situ.

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He, Z., Huang, Z. & Situ, H. Dynamics of quantum coherence in two-dimensional quantum walk on finite lattices. Eur. Phys. J. Plus 132, 299 (2017). https://doi.org/10.1140/epjp/i2017-11577-6

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