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Multipartite entanglement in four-qubit graph states

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Abstract

We consider a compendium of the non-trivial four-qubit graphs, derive their corresponding quantum states and classify them into equivalent classes. We use Meyer-Wallach measure and its generalizations to study block-partition and global entanglement in these states. We obtain several entanglement quantities for each graph state, which present a comprehensive characterization of the entanglement properties of the latter. As a result, a number of correlations between the graph structure and multipartite entanglement quantities have also been established.

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References

  1. M. Hein, W. Dur, J. Eisert, R. Raussendorf, M. Van den Nest, H.J. Briegel, Proc. Int. School Phys. Enrico Fermi. Quantum Computers, Algorithms and Chaos 162, 115 (2006)

  2. M. Hein, J. Eisert, H. Eisert, J. Briegel, Phys. Rev. A 69, 062311 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  3. S. Salimi, D. Karami, E. Salimi, Int J. Theor. Phys. 51, 2031 (2012)

    Article  MathSciNet  Google Scholar 

  4. M. Van den Nest, J. Dehaene, B. De Moor, Phys. Rev. A 69, 022316 (2004)

    Article  ADS  Google Scholar 

  5. D. Browne, H. Briegel, arXiv:0603226v2 (2006)

  6. D. Schlingemann, Quantum. Inf. Comput. 4, 287 (2004)

    MathSciNet  Google Scholar 

  7. H.J. Briegel, R. Raussendorf, Phys. Rev. Lett. 86, 910 (2001)

    Article  ADS  Google Scholar 

  8. M. Grassl, A. Klappenecker, M. Rotteler, in Proceedings of the IEEE International Symposium on Information Theory (Lausanne, 2002), p. 45

  9. D. Schlingemann, arXiv:0308022v1 (2003)

  10. W. Huang, Z. Wei, J. Phys. A 42, 295301 (2009)

    Article  MathSciNet  Google Scholar 

  11. D. Gottesman, arXiv:9705052v1, Ph.D. Thesis, California Insitute of Technology (1997)

  12. R. Raussendorf, H.J. Briegel, Phys. Rev. Lett. 86, 5188.(2000)

    Article  ADS  Google Scholar 

  13. E.T. Campbell, J. Fitzsimons, Int. J. Quantum Inf. 8, 219 (2010)

    Article  Google Scholar 

  14. S.M. Lee, H.S. Park, J. Cho, Y. Kang, J.Y. Lee, H. Kim, D.H. Lee, S.K. Choi, Opt. Express. 70, 6915 (2012)

    Article  ADS  Google Scholar 

  15. R. Raussendorf, D.E. Browne, H.J. Briegel, Phys. Rev. A 68, 022312 (2003)

    Article  ADS  Google Scholar 

  16. M.A. Nielsen, Rep. Math. Phys. 57, 147 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  17. B.A. Bell, M.S. Tame, A.S. Clark, R.W. Nock, W.J. Wadsworth, J.G. Rarity, New J. Phys. 15, 053030 (2013)

    Article  ADS  Google Scholar 

  18. M. Plesch, V. Buzek, Phys. Rev. A 67, 012322 (2003)

    Article  ADS  Google Scholar 

  19. W. Dur, Phys. Rev. A 63, 020303 (2001)

    Article  ADS  Google Scholar 

  20. M. Koashi, V. Buzek, N. Imoto, Phys. Rev. A 62, 050302(R) (2000)

    Article  ADS  MathSciNet  Google Scholar 

  21. S.J. Akhtarshenas, M. GharahiGhahi, arXiv:1003.2762v1 (2010)

  22. N. Paul, J.V. Menon, S. Karumanchi, S. Muralidharan, P.K. Panigrahi, Quant. Inf. Process. 10, 619 (2011)

    Article  MathSciNet  Google Scholar 

  23. D.Ch. Li, Z.L. Cao, Theor. Phys. 47, 464 (2007)

    Article  ADS  Google Scholar 

  24. O. Guhne, G. Toth, P. Hyllus, H.J. Briegel, Phys. Rev. Lett. 95, 120405 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  25. V. Scarani, A. Acin, E. Schenck, M. Aspelmeyer, Phys. Rev. A 71, 042325 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  26. R. Ceccarelli, G. Vallone, F.D. Martini, P. Mataloni, A. Cabello, Phys. Rev. Lett. 103, 160401 (2009)

    Article  ADS  Google Scholar 

  27. Wu. Chunfeng, Yeo. Ye, L.C. Kwek, C.H. Oh, Phys. Rev. A 75, 032332 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  28. B. Adhikari, S. Adhikari, S. Banerjee, arXiv:1205.2747v1 (2012)

  29. M. Horodecki, P. Horodecki, R. Horodecki, Phys. Lett. A 223, 1 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  30. S. Rai, J.R. Luthra, arXiv:0507263v1 (2005)

  31. W.K. Wootters, Phys. Rev. Lett. 80, 2245 (1998)

    Article  ADS  Google Scholar 

  32. D. Markham, A. Miyake, Sh. Virmani, New J. Phys. 9, 194 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  33. V. Vedral, M.B. Plenio, Phys. Lett. A 57, 1619 (1998)

    Google Scholar 

  34. P.J. Love, A.M. Van den Brink, A.Yu. Smirnov, M.H.S. Amin, M. Grajcar, E. Ilichev, A. Izmalkov, A.M. Zagoskin, Quantum. Inf. Process. 6, 187 (2007)

    Article  MathSciNet  Google Scholar 

  35. D.A. Meyer, N.R. Wallach, J. Math. Phys. 43, 4273 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  36. G.K. Brennen, Quantum. Inf. Comput. 3, 619 (2003)

    MathSciNet  Google Scholar 

  37. A.J. Scott, Phys. Rev. A 69, 052330 (2004)

    Article  ADS  Google Scholar 

Download references

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Correspondence to Mojtaba Jafarpour.

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Jafarpour, M., Assadi, L. Multipartite entanglement in four-qubit graph states. Eur. Phys. J. D 70, 62 (2016). https://doi.org/10.1140/epjd/e2016-60555-5

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