Advertisement

Distinguishing different classes of entanglement of three-qubit pure states

  • Chandan DattaEmail author
  • Satyabrata Adhikari
  • Arpan Das
  • Pankaj Agrawal
Regular Article

Abstract

Employing the Pauli matrices, we have constructed a set of operators, which can be used to distinguish six inequivalent classes of entanglement under stochastic local operation and classical communication (SLOCC) for three-qubit pure states. These operators have very simple structure and can be obtained from the Mermin’s operator with suitable choice of directions. Moreover, these operators may be implemented in an experiment to distinguish the types of entanglement present in a state. We show that the measurement of only one operator is sufficient to distinguish GHZ class from rest of the classes. It is also shown that it is possible to detect and classify other classes by performing a small number of measurements. We also show how to construct such observables in any basis. We also consider a few mixed states to investigate the usefulness of our operators. Furthermore, we consider the teleportation scheme of Lee et al. [Phys. Rev. A 72, 024302 (2005)] and show that the partial tangles and hence teleportation fidelity can be measured. We have also shown that these partial tangles can also be used to classify genuinely entangled state, biseparable state and separable state.

Graphical abstract

Keywords

Quantum Information 

References

  1. 1.
    N. Gisin, G. Ribordy, W. Tittel, H. Zbinden, Rev. Mod. Phys. 74, 145 (2002) ADSCrossRefGoogle Scholar
  2. 2.
    C.H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, W.K. Wootters, Phys. Rev. Lett. 70, 1895 (1993) ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    D. Bouwmeester, J-W Pan, K. Mattle, M. Eibl, H. Weinfurter, A. Zeilinger, Nature 390, 575 (1997) Google Scholar
  4. 4.
    C.H. Bennett, S.J. Wiesner, Phys. Rev. Lett. 69, 2881 (1992) ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    A. Harrow, P. Hayden, D. Leung, Phys. Rev. Lett. 92, 187901 (2004) ADSCrossRefGoogle Scholar
  6. 6.
    M.B. Plenio, S. Virmani, Quantum Inf. Comput. 7, 1 (2007) MathSciNetGoogle Scholar
  7. 7.
    R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki, Rev. Mod. Phys. 81, 865 (2009) ADSCrossRefGoogle Scholar
  8. 8.
    C. Datta, P. Agrawal, S.K. Choudhary, Phys. Rev. A 95, 042323 (2017) ADSCrossRefGoogle Scholar
  9. 9.
    V. Vedral, M.B. Plenio, Phys. Rev. A 57, 1619 (1998) ADSCrossRefGoogle Scholar
  10. 10.
    C.H. Bennett, H.J. Bernstein, S. Popescu, B. Schumacher, Phys. Rev. A 53, 2046 (1996) ADSCrossRefGoogle Scholar
  11. 11.
    N. Linden, S. Popescu, B. Schumacher, M. Westmoreland, https://doi.org/arXiv:quant-ph/9912039
  12. 12.
    G. Vidal, W. Dür, J.I. Cirac, Phys. Rev. Lett. 85, 658 (2000) ADSCrossRefGoogle Scholar
  13. 13.
    S. Wu, Y. Zhang, Phys. Rev. A 63, 012308 (2000) ADSCrossRefGoogle Scholar
  14. 14.
    C.H. Bennett, S. Popescu, D. Rohrlich, J.A. Smolin, A.V. Thapliyal, https://doi.org/arXiv:quant-ph/9908073
  15. 15.
    G. Vidal, J. Mod. Opt. 47, 355 (2000) ADSCrossRefGoogle Scholar
  16. 16.
    W. Dür, G. Vidal, J.I. Cirac, Phys. Rev. A 62, 062314 (2000) ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    A. Das, C. Datta, P. Agrawal, Phys. Lett. A 381, 3928 (2017) ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    M.-J. Zhao, T.-G. Zhang, X. Li-Jost, S.-M. Fei, Phys. Rev. A 87, 012316 (2013) ADSCrossRefGoogle Scholar
  19. 19.
    A. Acín, A. Andrianov, E. Jané, R. Tarrach, J. Phys. A: Math. Gen. 34, 6725 (2001) ADSCrossRefGoogle Scholar
  20. 20.
    A. Acín, D. Bruss, M. Lewenstein, A. Sanpera, Phys. Rev. Lett. 87, 040401 (2001) ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    S. Dogra, K. Dorai, Arvind, Phys. Rev. A 91, 022312 (2015) ADSCrossRefGoogle Scholar
  22. 22.
    S. Lee, J. Joo, J. Kim, Phys. Rev. A 72, 024302 (2005) ADSCrossRefGoogle Scholar
  23. 23.
    V. Coffman, J. Kundu, W.K. Wootters, Phys. Rev. A 61, 052306 (2000) ADSCrossRefGoogle Scholar
  24. 24.
    P. Rungta, V. Buzek, C.M. Caves, M. Hillery, G.J. Milburn, Phys. Rev. A 64, 042315 (2001) ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    D.P. Chi, K. Jeong, T. Kim, K. Lee, S. Lee, Phys. Rev. A 81, 044302 (2010) ADSCrossRefGoogle Scholar
  26. 26.
    S. Adhikari, A.S. Majumdar (2016), https://doi.org/arXiv:1602.02619
  27. 27.
    A. Acín, A. Andrianov, L. Costa, E. Jané, J.I. Latorre, R. Tarrach, Phys. Rev. Lett. 85, 1560 (2000) ADSCrossRefGoogle Scholar
  28. 28.
    F. Mintert, A. Buchleitner, Phys. Rev. Lett. 98, 140505 (2007) ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    O.J. Farías, G.H. Aguilar, A.V. Hernández, P.H.S. Ribeiro, L. Davidovich, S.P. Walborn, Phys. Rev. Lett. 109, 150403 (2012) ADSCrossRefGoogle Scholar
  30. 30.
    S. Popescu, Phys. Rev. Lett. 72, 797 (1994) ADSMathSciNetCrossRefGoogle Scholar
  31. 31.
    S. Massar, S. Popescu, Phys. Rev. Lett. 74, 1259 (1995) ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    A. Singh, H. Singh, K. Dorai, Arvind, https://doi.org/arXiv:1804.09320 (2018)

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Physics, Sachivalaya MargBhubaneswarIndia
  2. 2.Homi Bhabha National Institute, Training School ComplexMumbaiIndia
  3. 3.Delhi Technological University, Shahbad DaulatpurDelhiIndia

Personalised recommendations