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Preparing Greenberger-Horne-Zeilinger States by Lypunov Control

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Abstract

A scheme is proposed for preparing Greenberger-Horne-Zeilinger (GHZ) states by Lyapunov control based on quantum Zeno dynamics. The advantage of our method is that we use the square pulse to instead of the time-varying control fields and optimal the control processing which is shorter than the stimulated Raman adiabatic passage. The influence of cavity decay and spontaneous emission also be taken in account, the numerical simulation results show that it is immune to the cavity decay and emission of laser pulses. Additionally, we analyzed the preparation of the N-atom GHZ states with the same principle, which provides a scalable method for multi-qubit system in future.

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References

  1. Ekert, A.K.: Phys. Rev. Lett. 67, 661 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  2. Jia, X.J., Yan, Z.H., Duan, Z.Y., Su, X.L., Wang, H., Xie, C.D., Peng, K.C.: Phys. Rev. Lett. 109, 253604 (2012)

    Article  ADS  Google Scholar 

  3. Zheng, S.B.: Phys. Rev. Lett. 85, 2392 (2000)

    Article  ADS  Google Scholar 

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

    MATH  Google Scholar 

  5. Xia, Y., Song, J., Lu, P.M., Song, H.S.: J Opt. Soc. Am. B 27, A1 (2010)

    Article  Google Scholar 

  6. Bennett, C.H., Brassard, G., Crepeau, C., Jozsa, R., Peter, A., Wootter, W.: Phys. Rev. Lett. 70, 1895 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  7. Hillery, M., Buzek, V., Berthiaume, R.A.: Phys. Rev. A 59, 1829 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  8. Schneider, S., Milburn, G.J.: Phys. Rev. A 65, 042107 (2002)

    Article  ADS  Google Scholar 

  9. Kraus, B., Bǔchler, H.P., Diehl, S., Kantian, A., Micheli, A., Zoller, P.: Phys. Rev. A 78, 042307 (2008)

    Article  ADS  Google Scholar 

  10. Vacanti, G., Beige, A.: New J. Phys. 11, 083008 (2009)

    Article  ADS  Google Scholar 

  11. Verstraete, F., Wolf, M.M., Cirac, J.I.: Nat. Phys. 9, 633 (2009)

    Article  Google Scholar 

  12. Cho, J., Bose, S., Kim, M.S.: Phys. Rev. Lett. 106, 020504 (2011)

    Article  ADS  Google Scholar 

  13. Shao, X.Q., Chen, L., Zhang, S., Zhao, Y.F., Yeon, K.H.: Euro. Lett. 90, 50003 (2010)

    Article  ADS  Google Scholar 

  14. Xiao, Y.F., Zou, X.B., Guo, G.C.: Phys. Rev. A 75, 012310 (2007)

    Article  ADS  Google Scholar 

  15. Lamata, L., López, C.E., Lanyon, B.P., Bastin, T., Retamal, J.C., Solano, E.: Phys. Rev. A 87, 032325 (2013)

    Article  ADS  Google Scholar 

  16. Greenberger, D.M., Horne, M.A., Shimony, A., Zeilinger, A.: Am. J. Phys. 58, 1131 (2007)

    Article  ADS  Google Scholar 

  17. Zheng, S.B.: Eur. Phys. J. 54, 719 (2009)

    ADS  Google Scholar 

  18. Zheng, S.B.: Phys. Rev. Lett. 230404, 87 (2001)

    Google Scholar 

  19. Shi, Z.C., Xia, Y., Song, J., Song, H.S.: Quantum Inf. Comput. 12, 0215 (2012)

    MathSciNet  Google Scholar 

  20. Su, X.L., Tan, A.H., Jia, X.J., Zhang, J., Xie, C.D., Peng, K.C.: Phys. Rev. Lett. 98, 070502 (2007)

    Article  ADS  Google Scholar 

  21. Zhao, Z., Chen, Y.A., Zhang, A.N., Yang, T., Briegel, H.J., Pan J.W.: Nature 430, 54 (2004)

    Article  ADS  Google Scholar 

  22. Raimond, J.M., Brune, M., Haroche, S.: Rev. Mod. Phys. 73, 565 (2001)

    Article  ADS  Google Scholar 

  23. Chen, Y.H., Xia, Y., Song, J., Chen, Q.Q.: Sci. Rep. 5, 15616 (2015)

    Article  ADS  Google Scholar 

  24. Shan, W.J., Xia, Y., Chen, Y.H., Song, J.: Quantum Inf. Process 15, 2359 (2016)

    Article  MathSciNet  ADS  Google Scholar 

  25. Fewell, M.P., Shore, B.W., Bergmann, K.: Aust. J. Phys. 50, 281 (1997)

    Article  ADS  Google Scholar 

  26. Bergmann, K., Theuer, H., Shore, B.W.: Rev. Mod. Phys. 70, 1003 (1998)

    Article  ADS  Google Scholar 

  27. Vitanov, N.V., Halfmann, T., Shore, B.W., Bergmann, K.: Annu. Rev. Phys. Chem. 52, 763 (2001)

    Article  ADS  Google Scholar 

  28. Kral, P., Thanopulos, L., Shapiro, M.: Rev. Mod. Phys. 79, 53 (2007)

    Article  ADS  Google Scholar 

  29. Castro, A.O., Johnson, N.F., Quiroga, L.: Phys. Rev. A 70, 020301 (2004). (R)

    Article  Google Scholar 

  30. Zheng, S.B.: J. Opt. B Quantum Semiclass Opt. 7, 10 (2005)

    Article  ADS  Google Scholar 

  31. Li, W.A., Wei, L.F.: Qpt. Express 20, 13440 (2012)

    Article  ADS  Google Scholar 

  32. Hao, S.Y., Xia, Y., Song, J., An, N.B.: J. Opt. Soc. Am. B 30, 468 (2013)

    Article  ADS  Google Scholar 

  33. Chen, X., Lizuain, I., Ruschhaupt, A., Guéry-Odelin, D., Muga, J.G.: Phys. Rev. Lett. 105, 12303 (2010)

    Google Scholar 

  34. Torrontegui, E., Ibánêz, S., Modugno, S., Campo, A.D., Guéry-Odelin, D., Ruschhaupt, A., Chen, X., Muga, J.G.: Adv. Atomic mol. Opt. Phys. 62, 117 (2013)

    Article  ADS  Google Scholar 

  35. Campo, A.D.: Phys. Rev. Lett. 100502, 111 (2015)

    Google Scholar 

  36. Masuda, S., Nakamura, K.: Phys. Rev. A 84, 043434 (2011)

    Article  ADS  Google Scholar 

  37. Berry, M.V.: J. Phys. A 42, 365303 (2009)

    Article  MathSciNet  Google Scholar 

  38. Ji, Y.Q., Liu, Y.L., Zhou, S.J., Xiu, X.M., Dong, L., Dong, H.K., Gao, Y.J., Yi, X.X.: Phys. Rev. A 99, 023808 (2019)

    Article  ADS  Google Scholar 

  39. Wang, X.T., Schirmer, S.G.: Phys. Rev. A 80, 042305 (2009)

    Article  ADS  Google Scholar 

  40. Wang, X.T., Bayat, A., Bose, S., Schirmer, S.G.: Phys. Rev. A 82, 012330 (2010)

    Article  ADS  Google Scholar 

  41. Zhang, D.W., Qin, M., Yi, X.X.: Mod. Phys. Lett. B 32, 1850099 (2018)

    Article  ADS  Google Scholar 

  42. Zhang, D.W., Wang, W.: Mod. Phys. Lett. A 34, 1950227 (2019)

    Article  ADS  Google Scholar 

  43. Hou, S.C., Khan, M.A., Yi, X.X., Dong, D.Y., Petersen, I.R.: Phys. Rev. A 86, 022321 (2012)

    Article  ADS  Google Scholar 

  44. Shi, Z.C., Wang, L.C., Yi, X.X.: Quantum Inf. Process 15, 4939 (2016)

    Article  MathSciNet  ADS  Google Scholar 

  45. Shi, Z.C., Zhao, X.L., Yi, X.X.: Sci. Rep. 5, 13777 (2015)

    Article  ADS  Google Scholar 

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Acknowledgment

This work is supported by the National Natural Science Foundation of China, Grant Numbers: 11947085; Scientific Research Fundation of the Education Department of Jilin Province, Grants Number: JJKH20190764KJ; Scientific Research Fundation of the Education Department of Liaoning Province, Grants Number:L2020008; Nature Fund Guidance Plan of Liaoning Province 2019-ZD-0367; Program for Excellent Talents of Science and Technology in Yingkou Institute of Technology.

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Authors and Affiliations

  1. Department of Electrical Engineering, Yingkou Institute of Technology, Yingkou, 115014, China

    D. W. Zhang & S. J. Mu

  2. Department of Basic, Yingkou Institute of Technology, Yingkou, 115014, China

    J. H. Teng

  3. Institute for Interdisciplinary Quantum Information Technology, Jilin Engineering Normal University, Changchun, 334001, China

    Hong Li

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  1. D. W. Zhang
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  2. J. H. Teng
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  3. S. J. Mu
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  4. Hong Li
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Correspondence to Hong Li.

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Zhang, D.W., Teng, J.H., Mu, S.J. et al. Preparing Greenberger-Horne-Zeilinger States by Lypunov Control. Int J Theor Phys 60, 1539–1549 (2021). https://doi.org/10.1007/s10773-021-04776-2

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  • DOI: https://doi.org/10.1007/s10773-021-04776-2

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