Skip to main content
SpringerLink
Log in

Operational criterion for controlled dense coding with non-trivial tripartite entangled states

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

In this paper, we provide an operational criterion for controlled dense coding (CDC) with a general class of three-qubit partially entangled states. A general three-qubit pure entangled state can be classified into two inequivalent classes according to their genuine tripartite entanglement. We claim that if a three-qubit state shows entanglement characteristic similar to Greenberger–Horne–Zeilinger (GHZ)-class, then such non-trivial tripartite states are useful in CDC whereas states belonging to the W-class are not useful for that. We start with a particular class of non-trivial partially entangled states belonging to the GHZ-class and show that they are effective in CDC. Then we cite several other examples of different types of tripartite entangled states to support our conjecture.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

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

    Article  ADS  MathSciNet  Google Scholar 

  2. K Mattle, H Weinfurter, P G Kwiat and A Zeilinger, Phys. Rev. Lett. 76, 4656 (1996)

    Article  ADS  Google Scholar 

  3. J-C Hao, C-F Li and G-C Guo, Phys. Rev. A 63, 054301 (2001)

    Article  ADS  Google Scholar 

  4. D Bouwmeester, J-W Pan, M Daniell, H Weinfurter and A Zeilinger, Phys. Rev. Lett. 82, 1345 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  5. A Acin, E Jane, W Dür and G Vidal, Phys. Rev. Lett. 85, 4811 (2000)

    Article  ADS  Google Scholar 

  6. W Dür, G Vidal and J I Cirac, Phys. Rev. A 62, 062314 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  7. C H Bennett, H J Bernstein, S Popescu and B Schumacher, Phys. Rev. A 53, 2046 (1996)

    Article  ADS  Google Scholar 

  8. X-P Zang, M Yang, C-Q Du, Mn Wang, S-D Fang and Z-L Cao, Pramana – J. Phys. 86, 1009 (2016)

    Article  ADS  Google Scholar 

  9. H Fu, P-C Ma, G-B Chen, X-W Li and Y-B Zhan, Pramana – J. Phys. 88: 92 (2017)

    Article  ADS  Google Scholar 

  10. C Fu, Y Xia, B Liu and S Zhang, J. Korean Phys. Soc. 46, 1080 (2005)

    Google Scholar 

  11. D-Y Jiang, R S Wu, S S Li and Z S Wang, Int. J. Theor. Phys. 48, 2297 (2009)

    Article  Google Scholar 

  12. X-W Liu, Int. J. Theor. Phys. 54, 1253 (2015)

    Article  Google Scholar 

  13. J Liu, Z-W Mo and S-Q Sun, Int. J. Theor. Phys. 55, 2182 (2016)

    Article  Google Scholar 

  14. D Liu, Int. J. Theor. Phys. 54, 2784 (2015)

    Article  Google Scholar 

  15. Y-Y Nie, Y-H Li, X-P Wang and M-H Sang, Quantum Inf. Process. 12, 1851 (2013)

    Article  ADS  Google Scholar 

  16. S Roy and B Ghosh, Int. J. Quantum Inf. 13, 1550033 (2015)

    Article  MathSciNet  Google Scholar 

  17. D M Greenberger, M A Horne and A Zeilinger, Bell’s theorem, quantum theory and conceptions of the universe edited by M Kafatos (Springer, Netherlands, 1989), Fund. Theor. of Phys., ISBN 978-94-017-0849-4

  18. X-H Li and S Ghose, Phys. Rev. A 90, 052305 (2014)

    Article  ADS  Google Scholar 

  19. V Coffman, J Kundu and W K Wootters, Phys. Rev. A 61, 052306 (2000)

    Article  ADS  Google Scholar 

  20. R Lohmayer, A Osterloh, J Siewert and A Uhlmann, Phys. Rev. Lett. 97, 260502 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  21. C Eltschka, O Osterloh, J Siewert and A Uhlmann, New J. Phys. 10, 043014 (2008)

    Article  ADS  Google Scholar 

  22. A K Pati, P Parashar and P Agrawal, Phys. Rev. A 72, 012329 (2005)

    Article  ADS  Google Scholar 

  23. L Li and D Qiu, J. Phys. A 40, 10871 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  24. J S Kim, G Gour and B C Sanders, Contemp. Phys. 53, 417 (2012)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

M M Ali acknowledges the support from the Ministry of Science and Technology of Taiwan and the Physics Division of National Center for Theoretical Sciences, Taiwan.

Author information

Authors and Affiliations

  1. Department of Mathematics, Techno India, EM 4 / 1, Salt Lake, Kolkata,  700 091, India

    Sovik Roy

  2. Department of Physics, Vivekananda College for Women, Barisha, Kolkata,  700 008, India

    Biplab Ghosh

  3. Physics Division, National Center for Theoretical Sciences, National Tsing Hua University,  Hsinchu,  30013, Taiwan

    Md Manirul Ali

Authors
  1. Sovik Roy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Biplab Ghosh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Md Manirul Ali
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sovik Roy.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Roy, S., Ghosh, B. & Ali, M.M. Operational criterion for controlled dense coding with non-trivial tripartite entangled states. Pramana - J Phys 91, 50 (2018). https://doi.org/10.1007/s12043-018-1630-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12043-018-1630-1

Keywords

PACS Nos

Search

Navigation