Skip to main content
SpringerLink
Log in

Genuine three-partite entanglement in coherent states via permutation and parity symmetries

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

By using the works, Spiridonov (Phys Rev A 52:1909, 1995), and Wang et al. (J Phys A Math Gen 33:7451, 2000), we propose an approach to obtain genuine three-partite entangled coherent states in which the permutation symmetry and the parity one play crucial roles. We exploit the permutation and parity symmetry to construct entanglement in the standard coherent states of a system composed of three-mode bosonic field and three identical atoms. It is shown that by making use of entanglement witnesses (EW) based on GHZ-states the reduced density matrices of the three-mode bosonic field and three-atomic subsystems, after encoding as three-qubit systems, in some range of their respective parameters, are genuinely entangled.

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. Horodecki R., Horodecki P., Horodecki M., Horodecki K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. Bennett C.H., Brassard G., Crepeau C., Jozsa R., Peres A., Wootters W.K.: Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70, 1895 (1993)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. Ekert A.K.: Quantum cryptography based on Bells theorem. Phys. Rev. Lett. 67, 661 (1991)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. Bennett C.H., Wiesner S.J.: Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett. 69, 2881 (1992)

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    MATH  Google Scholar 

  6. Yang Y., Xu J., Chen H., Zhu S.Y.: Long-lived entanglement between two distant atoms via left-handed materials. Phys. Rev. A 82, 030304 (2010)

    Article  ADS  Google Scholar 

  7. Wang J., Pan Q., Jing J.: Projective measurements and generation of entangled Dirac particles in Schwarzschild spacetime. Ann. Phys. (NY) 325, 1190 (2010)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. Pathak P.K., Hughes S.: Cavity-assisted fast generation of entangled photon pairs through the biexciton-exciton cascade. Phys. Rev. B 80, 155325 (2009)

    Article  ADS  Google Scholar 

  9. Cho J., Angelakis D.G., Bose S.: Heralded generation of entanglement with coupled cavities. Phys. Rev. A 78, 022323 (2008)

    Article  ADS  Google Scholar 

  10. Petitjean C., Jacquod P.: Lyapunov generation of entanglement and the correspondence principle. Phys. Rev. Lett. 97, 194103 (2006)

    Article  ADS  Google Scholar 

  11. Yuan C.H., Ou Y.C., Zhang Z.M.: Generation of GHZ-type and W-type entangled coherent states of three-cavity fields. Chin. Phys. Lett. 23(7), 1695 (2006)

    Article  ADS  Google Scholar 

  12. Hyunseok J., Nguyen B.A.: Greenberger-Horne-Zeilinger-type and W-type entangled coherent states: generation and Bell-type inequality tests without photon counting. Phys. Rev. A 74, 022104 (2006)

    Article  MathSciNet  Google Scholar 

  13. Yang M., Cao Z.-L.: Quantum information processing using coherent states in cavity QED. Phys. A 366, 243 (2006)

    Article  MathSciNet  Google Scholar 

  14. Nguyen B.A.: Optimal processing of quantum information via W-type entangled coherent states. Phys. Rev. A 69, 022315 (2004)

    Article  Google Scholar 

  15. Nguyen B.A.: Cluster-type entangled coherent states: generation and application. Phys. Rev. A 80, 042316 (2009)

    Article  Google Scholar 

  16. Yuan C.H., Ou Y.C., Zhang Z.M.: Generation of GHZ-type and W-type entangled coherent states of three-cavity fields. Chin. Phys. Lett. 23(7), 1695 (2006)

    Article  ADS  Google Scholar 

  17. Wang X., Feng M., Sanders Barry C.: Multipartite entangled states in coupled quantum dots and cavity QED. Phys. Rev. A 67, 022302 (2003)

    Article  ADS  Google Scholar 

  18. Solano E., Agarwal G.S., Walther H.: Strong-driving-assisted multipartite entanglement in cavity QED. Phys. Rev. Lett. 90, 027903 (2003)

    Article  ADS  Google Scholar 

  19. Wang X., Sanders B.C.: Multipartite entangled coherent states. Phys. Rev. A 65, 012303 (2001)

    Article  MathSciNet  ADS  Google Scholar 

  20. Peres A.: Separability criterion for density matrices. Phys. Rev. Lett. 77, 1413 (1996)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. Zyczkowski K., Horodecki P., Sanpera A., Lewenstein M.: Volume of the set of separable states. Phys. Rev. A 58, 883 (1998)

    Article  MathSciNet  ADS  Google Scholar 

  22. Vidal G., Werner R.F.: Computable measure of entanglement. Phys. Rev. A 65, 032314 (2002)

    Article  ADS  Google Scholar 

  23. Wootters W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245 (1998)

    Article  ADS  Google Scholar 

  24. Greenberger, D.M., Horne, M., Zeilinger, A.: In: Kafatos, M. (ed) Bell’s Theorem, Quantum Theory, and Conceptions of the Universe. Kluwer Academic, Dordrecht (1989)

  25. Bouwmeester D., Ekert A., Zeilinger A.: The Physics of Quantum Information. Springer, Heidelberg (2000)

    MATH  Google Scholar 

  26. Horodecki M., Horodecki P., Horodecki R.: Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A 223, 1 (1996)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. Terhal B.M.: Bell inequalities and the separability criterion. Phys. Lett. A 271, 319 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  28. Terhal B.M.: A family of indecomposable positive linear maps based on entangled quantum states. Linear Algebra Appl. 323, 61 (2000)

    Article  MathSciNet  Google Scholar 

  29. Jafarizadeh M.A., Behzadi N.: Entanglement via permutation symmetry and reflection invariance of angular momentum algebra. Eur. Phys. J. D 55, 729–744 (2009)

    Article  ADS  Google Scholar 

  30. Jafarizadeh M.A., Behzadi N., Akbari Y.: Entanglement witnesses and characterizing entanglement properties of some PPT states. Eur. Phys. J. D 55, 197–203 (2009)

    Article  ADS  Google Scholar 

  31. Acin A., Brus D., Lewenstein M., Sanpera A.: Classification of mixed three-qubit states. Phys. Rev. Lett. 87, 040401 (2001)

    Article  MathSciNet  ADS  Google Scholar 

  32. Bourennance M., Eibl M., Kurtsiefer C., Gaertner S., Weinfurter H., Guhne O., Hyllus P., Brus D., Lewensiein M., Sanpera A.: Experimental detection of multipartite entanglement using witness operators. Phys. Rev. Lett. 92, 087902 (2004)

    Article  ADS  Google Scholar 

  33. Sivakumar S.: Entanglement of fields in coupled cavities: effects of pumping and fluctuations. Phys. Lett. A 374, 1793 (2010)

    Article  ADS  MATH  Google Scholar 

  34. Guhne O., Hyllus P.: Investigating three qubit entanglement with local measurements. Int. J. Theor. Phys. 42(5), 1001 (2003)

    Article  MathSciNet  Google Scholar 

  35. Toth G., Guhne O.: Detecting genuine multipartite entanglement with two local measurements. Phys. Rev. Lett. 94, 060501 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  36. Spiridonov V.: Universal superpositions of coherent states and self-similar potentials. Phys. Rev. A 52, 1909 (1995)

    Article  ADS  Google Scholar 

  37. Wang X.G., Sanders B.C., Pan S.H.: Entangled coherent states for systems with SU(2) and SU(1,1) symmetries. J. Phys. A Math. Gen. 33, 7451 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research Institute for Fundamental Sciences, University of Tabriz, 51666-16471, Tabriz, Iran

    N. Behzadi

Authors
  1. N. Behzadi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. Behzadi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Behzadi, N. Genuine three-partite entanglement in coherent states via permutation and parity symmetries. Quantum Inf Process 12, 21–32 (2013). https://doi.org/10.1007/s11128-011-0352-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-011-0352-9

Keywords

Search

Navigation