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Measure and detection of genuine multipartite entanglement for n-partite systems

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Abstract

We investigate genuine multipartite entanglement (GME) in n-partite systems. The norms of the correlation vectors are used as a powerful tool to dealing with the detection of GME for n-partite quantum systems. A sufficient condition for detecting GME in general multipartite systems is presented. Moreover, an effective lower bound of the GME concurrence is derived, which gives a useful way to measure the GME. Several examples are considered to show the effectiveness of the criterion and the lower bound of GME concurrence.

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References

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

    MATH  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  3. M. Hillery, V. Buz̆ek, V.A. Berthiaume, Phys. Rev. A 59, 1829 (1999)

  4. N. Gisin, G. Ribordy, W. Tittel, H. Zbinden, Rev. Mod. Phys. 74, 145 (2002)

    Article  ADS  Google Scholar 

  5. C.H. Bennett, S.J. Wiesner, Phys. Rev. Lett. 69, 2881 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  6. C.H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, W.K. Wootters, Phys. Rev. Lett. 70, 1895 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  7. O. Gühne, G. Tóth, Phys. Rep. 474, 1 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  8. R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki, Rev. Mod. Phys. 81, 865 (2009)

    Article  ADS  Google Scholar 

  9. A.C. Doherty, P.A. Parrilo, F.M. Spedalieri, Phys. Rev. A 71, 032333 (2005)

    Article  ADS  Google Scholar 

  10. R. Raussendorf, H.J. Briegel, Phys. Rev. Lett. 86, 5188 (2001)

    Article  ADS  Google Scholar 

  11. M. Murao, D. Jonathan, M.B. Plenio, V. Vedral, Phys. Rev. A 59, 156 (1999)

    Article  ADS  Google Scholar 

  12. V. Scarani, N. Gisin, Phys. Rev. Lett. 87, 117901 (2001)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  14. Y. Yeo, W.K. Chua, Phys. Rev. Lett. 96, 060502 (2006)

    Article  ADS  Google Scholar 

  15. P.X. Chen, S.Y. Zhu, G.C. Guo, Phys. Rev. A 74, 032324 (2006)

    Article  ADS  Google Scholar 

  16. M. Huber, F. Mintert, A. Gabriel, B.C. Hiesmayr, Phys. Rev. Lett. 104, 210501 (2010)

    Article  ADS  Google Scholar 

  17. M. Huber, R. Sengupta, Phys. Rev. Lett. 113, 100501 (2014)

    Article  ADS  Google Scholar 

  18. J.I. de Vicente, M. Huber, Phys. Rev. A 84, 062306 (2011)

    Article  ADS  Google Scholar 

  19. J.Y. Wu, H. Kampermann, D. Bruß, C. Klöckl, M. Huber, Phys. Rev. A 86, 022319 (2012)

    Article  ADS  Google Scholar 

  20. M. Huber, M. Perarnau-Llobet, J.I. de Vicente, Phys. Rev. A 88, 042328 (2013)

    Article  ADS  Google Scholar 

  21. B. Jungnitsch, T. Moroder, O. Gühne, Phys. Rev. Lett. 106, 190502 (2011)

    Article  ADS  Google Scholar 

  22. Z.H. Ma, Z.H. Chen, J.L. Chen, C. Spengler, A. Gabriel, M. Huber, Phys. Rev. A 83, 062325 (2011)

    Article  ADS  Google Scholar 

  23. Z.H. Chen, Z.H. Ma, J.L. Chen, S. Severini, Phys. Rev. A 85, 062320 (2012)

    Article  ADS  Google Scholar 

  24. Y. Hong, T. Gao, F.L. Yan, Phys. Rev. A 86, 062323 (2012)

    Article  ADS  Google Scholar 

  25. P. van Loock, A. Furusawa, Phys. Rev. A 67, 052315 (2003)

    Article  ADS  Google Scholar 

  26. M.J. Zhao, T.G. Zhang, X.Q. Li-Jost, S.M. Fei, Phys. Rev. A 87, 012316 (2013)

    Article  ADS  Google Scholar 

  27. M. Li, J. Wang, S.Q. Shen, Z.H. Chen, S.M. Fei, Sci. Rep. 7, 17274 (2017)

    Article  ADS  Google Scholar 

  28. M. Li, S.M. Fei, X.Q. Li-Jost, H. Fan, Phys. Rev. A 92, 062338 (2015)

    Article  ADS  Google Scholar 

  29. M. Li, L.X. Jia, J. Wang, S.Q. Shen, S.M. Fei, Phys. Rev. A 96, 052314 (2017)

    Article  ADS  Google Scholar 

  30. J.Y. Zhao, H. Zhao, N.H. Jing, S.M. Fei, Int. J. Theor. Phys. 58, 3181–3191 (2019)

    Article  Google Scholar 

  31. G. Kimura, Phys. Lett. A 314, 339 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  32. T.G. Kolda, B.W. Bader, SIAM Rev. 51, 455 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  33. R.A. Horn, C.R. Johnson, Topics in Matrix Analysis (Cambridge University Press, New York, 1994)

    MATH  Google Scholar 

  34. W. Xu, C.J. Zhu, Z.J. Zheng, S.M. Fei, Quantum Inf. Process. 19, 200 (2020)

    Article  ADS  Google Scholar 

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Acknowledgements

This work is supported by Key Research and Development Project of Guangdong Province under Grant No.2020B0303300001 and the Guangdong Basic and Applied Basic Research Foundation under Grant No.2020B1515310016 and the NSF of China under Grant Nos.11675113, the Key Project of Beijing Municipal Commission of Education (Grant No.KZ201810028042), Beijing Natural Science Foundation (Z190005), and Academy for Multidisciplinary Studies, Capital Normal University.

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Authors and Affiliations

  1. Department of Mathematics, South China University of Technology, Guangzhou, 510640, People’s Republic of China

    Wen Xu & Zhu-Jun Zheng

  2. Laboratory of Quantum Science and Engineering, South China University of Technology, Guangzhou, 510641, People’s Republic of China

    Wen Xu & Zhu-Jun Zheng

  3. College of Mathematics and Physics Science, Hunan University of Arts and Science, Changde, 415000, People’s Republic of China

    Chuan-Jie Zhu

  4. Department of Physics, Renmin University of China, Beijing, 100872, People’s Republic of China

    Chuan-Jie Zhu

  5. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, People’s Republic of China

    Shao-Ming Fei

  6. Max-Planck-Institute for Mathematics in the Sciences, 04103, Leipzig, Germany

    Shao-Ming Fei

Authors
  1. Wen Xu
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  2. Zhu-Jun Zheng
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  3. Chuan-Jie Zhu
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  4. Shao-Ming Fei
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Correspondence to Zhu-Jun Zheng.

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Xu, W., Zheng, ZJ., Zhu, CJ. et al. Measure and detection of genuine multipartite entanglement for n-partite systems. Eur. Phys. J. Plus 136, 5 (2021). https://doi.org/10.1140/epjp/s13360-020-01036-w

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