Quantum Information Processing

, Volume 14, Issue 2, pp 593–606 | Cite as

Generation of some entangled states of the cavity field

  • S. R. Miry
  • M. K. Tavassoly
  • R. Roknizadeh


In this paper, we suggest a scheme which can produce various types of entangled states of the cavity field. In the scheme, cavities with different circumstances which evolve in time are utilized. It is shown that if two cavities are arranged in a way that, the first cavity is governed by the Jaynes–Cummings (JC) and the other with anti-Jaynes–Cummings (anti-JC) Hamiltonian, entangled EPR state of the cavity field is generated. Also, the proposal can be extended to the multi-cavity case, where the cavities are arranged such that their time evolutions change alternately from JC to anti-JC Hamiltonian. From this configuration, three- and four-partite GHZ states can be generated. At last, it is illustrated that in the multi-cavity set up if one prepares all cavities with the same time evolution property, \(W\) state can be produced. An important feature of this scheme is the fact that the result of the processes is independent of the result of atomic detection.


Jaynes–Cummings interaction Anti-Jaynes–Cummings interaction Entangled state EPR state GHZ state 



The authors would like to thank the referees for their helpful comments and suggestions which satisfactorily improved the contents of the paper.


  1. 1.
    Pan, J.-W., Chen, Z.-B., Lu, C.-Y., Weinfurter, H., Zeilinger, A., Zukowski, M.: Multiphoton entanglement and interferometry. Rev. Mod. Phys. 84, 777 (2012)ADSCrossRefGoogle Scholar
  2. 2.
    Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47(10), 777–780 (1935)ADSCrossRefMATHGoogle Scholar
  3. 3.
    Greenberger, D.M., Horne, M., Zeilinger, A.: Bell’s Theorem, Quantum Theory and Conceptions of the Universe. Kluwer, Dordrecht (1989)Google Scholar
  4. 4.
    Dür, W., Vidal, G., Cirac, J.I.: Three qubits can be entangled in two inequivalent ways. Phys. Rev. A 62(6), 062314 (2000)ADSCrossRefMathSciNetGoogle Scholar
  5. 5.
    Raussendorf, R., Briegel, H.J.: A one-way quantum computer. Phys. Rev. Lett. 86(22), 5188 (2001)ADSCrossRefGoogle Scholar
  6. 6.
    Nielsen, M.A.: Optical quantum computation using cluster states. Phys. Rev. Lett. 93(4), 040503 (2004)Google Scholar
  7. 7.
    Sun, L.-H., Li, G.-X.: Preparation of four-mode cluster states with distant atomic ensembles. Phys. Rev. A 85(6), 065801 (2012)ADSCrossRefGoogle Scholar
  8. 8.
    Sagi, Y.: Scheme for generating Greenberger-Horne-Zeilinger-type states of n photons. Phys. Rev. A 68(4), 042320 (2003)ADSCrossRefGoogle Scholar
  9. 9.
    Rosa Silva, J.B., Ramos, R.V.: Smart generation of a tripartite GHZ-type state for coherent state qubit. Opt. Commun. 281(9), 2705 (2008)ADSCrossRefGoogle Scholar
  10. 10.
    Xia, Y., Lu, P.-M., Zeng, Y.-Z.: Effective protocol for preparation of N-photon GreenbergerHorneZeilinger states with conventional photon detectors. Quantum Inf. Process. 11(2), 6502–6511 (2012)CrossRefGoogle Scholar
  11. 11.
    Sharma, S.S.: Tripartite GHZ state generation with trapped ion in an optical cavity. Phys. Lett. A 311(2–3), 111–114 (2003)ADSCrossRefMathSciNetGoogle Scholar
  12. 12.
    Gonta, D., Fritzsche, S., Radtke, T.: Generation of four-partite Greenberger-Horne-Zeilinger and W states by using a high-finesse bimodal cavity. Phys. Rev. A 77(6), 062312 (2008)ADSCrossRefGoogle Scholar
  13. 13.
    Xu, P., Wang, D., Ye, L.: Generation of three-atom Greenberger-Horne-Zeilinger entangled states based on separate cavities. Opt. Commun. 297, 204209 (2013)Google Scholar
  14. 14.
    Yeo, Y., Chua, W.K.: Teleportation and dense coding with genuine multipartite entanglement. Phys. Rev. Lett. 96(6), 060502 (2006)ADSCrossRefGoogle Scholar
  15. 15.
    Jung, E., Hwang, M.-R., Ju, Y.H., Kim, M.-S., Yoo, S.-K., Kim, H., Park, D., Son, J.-W., Tamaryan, S., Cha, S.-K.: Greenberger-Horne-Zeilinger versus W states: quantum teleportation through noisy channels. Phys. Rev. A 78(1), 012312 (2008)ADSCrossRefGoogle Scholar
  16. 16.
    Wang, L.-Q., Zha, X.-W.: Two schemes of teleportation one-particle state by a three-particle GHZ state. Opt. Commun. 283(20), 4118 (2010)ADSCrossRefGoogle Scholar
  17. 17.
    Lu, C.-Y., Yang, T., Pan, J.-W.: Experimental multiparticle entanglement swapping for quantum networking. Phys. Rev. Lett. 103(2), 020501 (2009)ADSCrossRefGoogle Scholar
  18. 18.
    Hu, M.-L.: Robustness of GreenbergerHorneZeilinger and W states for teleportation in external environments. Phys. Lett. A 375(5), 922–926 (2011)ADSCrossRefGoogle Scholar
  19. 19.
    Druß, D., Divincenzo, D.P., Ekert, A., Fuchs, C.A., Macchiavello, C., Smolin, J.A.: Optimal universal and state-dependent quantum cloning. Phys. Rev. A 57(4), 2368 (1998)ADSCrossRefGoogle Scholar
  20. 20.
    Zheng, S.-B.: Splitting quantum information via W states. Phys. Rev. A 74(5), 054303 (2006)ADSCrossRefGoogle Scholar
  21. 21.
    Agrawal, P., Pati, A.: Perfect teleportation and superdense coding with W states. Phys. Rev. A 74(6), 062320 (2006)ADSCrossRefGoogle Scholar
  22. 22.
    Chen, L., Chen, Y.-X.: Classification of GHZ-type, W-type, and GHZ-W-type multiqubit entanglement. Phys. Rev. A 74(6), 062310 (2006)ADSCrossRefMathSciNetGoogle Scholar
  23. 23.
    Rai, A., Agarwal, G.S.: Possibility of coherent phenomena such as Bloch oscillations with single photons via W states. Phys. Rev. A 79(5), 053849 (2009)ADSCrossRefGoogle Scholar
  24. 24.
    Perez-Leija, A., Hernandez-Herrejon, J.C., Moya-Cessa, H., Szameit, A., Christodoulides, D.N.: Generating photon-encoded W states in multiport waveguide-array systems. Phys. Rev. A 87(1), 013842 (2013)ADSCrossRefGoogle Scholar
  25. 25.
    Deng, Z.J., Feng, M., Gao, K.L.: Simple scheme for generating an \(n\)-qubit W state in cavity QED. Phys. Rev. A 73(1), 014302 (2006)ADSCrossRefGoogle Scholar
  26. 26.
    Cardoso, W.B., Qiang, W.C., Avelar, A.T., Baseia, B.: Generation of two-photon EPR and W states. J. Phys. B At. Mol. Opt. Phys. 43, 155502 (2010)ADSCrossRefGoogle Scholar
  27. 27.
    Li, J.-G., Zou, J., Cai, J.-F., Shao, B.: Preparation of a \(2n\)-qubit W state via entanglement transfer. Phys. Lett. A 361(1–2), 59–62 (2007)ADSCrossRefMATHMathSciNetGoogle Scholar
  28. 28.
    Gonta, D., Fritzsche, S.: Multipartite W states for chains of atoms conveyed through an optical cavity. Phys. Rev. A 81(2), 022326 (2010)ADSCrossRefGoogle Scholar
  29. 29.
    Wang, H.-F., Zhang, S., Yi, X.X., Ji, X., Yeon, K.-H.: Robust and scalable scheme to generate multipartite atom–photon and atom–atom entangled W states by interference. J. Opt. Soc. Am. B 29(2), 257–261 (2012)ADSCrossRefGoogle Scholar
  30. 30.
    Chen, A., Deng, L.: Scheme for generation of W and W-like states of nonidentical particles and their application in teleportation. Quantum Inf. Process. 6(4), 221–228 (2007)CrossRefMATHMathSciNetGoogle Scholar
  31. 31.
    An, N.B.: Optimal processing of quantum information via W-type entangled coherent states. Phys. Rev. A 69(2), 022315 (2004)ADSCrossRefGoogle Scholar
  32. 32.
    Jeong, H., An, N.B.: Greenberger-Horne-Zeilinger-type and W-type entangled coherent states: generation and Bell-type inequality tests without photon counting. Phys. Rev. A 74(2), 022104 (2006)ADSCrossRefMathSciNetGoogle Scholar
  33. 33.
    Yuan, C.-H., Ou, Y.-C., Zhang, Z.-M.: A scheme for preparation of W-Type entangled coherent state of three-cavity fields. Chin. Phys. Lett. 23(7), 1695 (2006)ADSCrossRefGoogle Scholar
  34. 34.
    Solano, E., Agarwal, G.S., Walther, H.: Strong-driving-assisted multipartite entanglement in cavity QED. Phys. Rev. Lett. 90(2), 027903 (2003)ADSCrossRefGoogle Scholar
  35. 35.
    Klimov, A.B., Chumakov, S.M.: A Group-Theoretical Approach to Quantum Optics. Wiley-VCH Verlag GmbH Co. KGaA, Weinheim (2009)CrossRefGoogle Scholar
  36. 36.
    Domokos, P., Raimond, J.M., Brune, M., Haroche, S.: Simple cavity-QED two-bit universal quantum logic gate: the principle and expected performances. Phys. Rev. A 52(5), 35543559 (1995)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Atomic and Molecular Group, Faculty of PhysicsYazd UniversityYazdIran
  2. 2.The Laboratory of Quantum Information ProcessingYazd UniversityYazdIran
  3. 3.Department of PhysicsUniversity of IsfahanIsfahanIran

Personalised recommendations