Skip to main content
Log in

Effective scheme for generation of \(N\)-dimension atomic Greenberger–Horne–Zeilinger states

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

In this paper, we propose an effective scheme for generation of \(N\)-dimension atomic Greenberger–Horne–Zeilinger states with the controlled phase flip gates. The successful probability of our scheme is 100 % in principle. The scheme is implemented with simple linear optical elements, delay lines and polarization-independent circulators. We discuss the feasibility of the setups, concluding that the scheme is feasible with current technology.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Zheng, S.B., Guo, G.C.: Teleportation of atomic states within cavities in thermal states. Phys. Rev. A 63, 044302 (2001)

    Article  ADS  Google Scholar 

  2. Bennett, C.H., Divincenzo, D.P.: Quantum information and computation. Nature (London) 404, 247 (2000)

    Article  ADS  Google Scholar 

  3. Deng, F.G., Long, G.L.: Two-step quantum direct communication protocol using the Einstein–Podolsky–Rosen pair block. Phys. Rev. A 68, 042317 (2003)

    Article  ADS  Google Scholar 

  4. Kempe, J.: Multiparticle entanglement and its applications to cryptography. Phys. Rev. A 60, 910 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  5. Hillery, M., Bužek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  6. 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 

  7. Shi, B.S., Tomita, A.: Teleportation of an unknown state by W state. Phys. Lett. A 296, 161 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. Gorbachev, V.N., Trubilko, A.I., Rodichkina, A.A., Zhiliba, A.I.: Can the states of the W-class be suitable for teleportation. Phys. Lett. A 314, 267 (2003)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. 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 

  10. Bužek, V., Hillery, M.: Crossed-field hydrogen atom and the three-body Sun–Earth–Moon problem. Phys. Rev. A 54, 1884 (1996)

    Article  MathSciNet  ADS  Google Scholar 

  11. Greenberger, D.M., Horne, M.A., Zeilinger, A.: In: Kafatos, M. (ed.) Bell’s Theorem, Quantum Theory, and Conceptions of the Universe, p. 69. Kluwer, Dordrecht (1989)

  12. Bell, J.S.: On the Einstein–Podolsky–Rosen paradox. Physics (New York: Long Island City) 1, 195 (1964)

  13. Karlsson, A., Bourennane, M.: Quantum teleportation using three-particle entanglement. Phys. Rev. A 58, 4394 (1998)

    Article  MathSciNet  ADS  Google Scholar 

  14. Jung, E., Hwang, M.R., Ju, Y.H., Kim, M.S., Yoo, S.K., Kim, H.S., Park, D.: Greenberger–Horne–Zeilinger versus W states: quantum teleportation through noisy channels. Phys. Rev. A 78, 012312 (2008)

    Article  ADS  Google Scholar 

  15. Cleve, R., Gottesman, D., Lo, H.K.: How to share a quantum secret. Phys. Rev. Lett. 83, 648 (1999)

    Article  ADS  Google Scholar 

  16. Yu, C.S., Yi, X.X., Song, H.S., Mei, D.: Robust preparation of Greenberger–Horne–Zeilinger and W states of three distant atoms. Phys. Rev. A 75, 044301 (2007)

    Article  ADS  Google Scholar 

  17. Xia, Y., Song, J., Song, H.S.: Linear optical protocol for preparation of \(N\)-photon Greenberger–Horne–Zeilinger state with conventional photon detectors. Appl. Phys. Lett. 92, 021127 (2008)

    Article  ADS  Google Scholar 

  18. Xia, Y., Lu, P.M., Zeng, Y.Z.: Effective protocol for preparation of N-photon Greenberger–Horne– Zeilinger states with conventional photon detectors. Quantum Inf. Process. 11(2), 605 (2012)

    Article  Google Scholar 

  19. Xia, Y., Hao, S.Y., Dong, Y.J., Song, J.: Effective schemes for preparation of Greenberger–Horne–Zeilinger and W maximally entangled states with cross-Kerr nonlinearity and parity-check measurement. Appl. Phys. B. 110, 551 (2013)

    Article  ADS  Google Scholar 

  20. Sagi, Y.: Scheme for generating Greenberger–Horne–Zeilinger-type states of n photons. Phys. Rev. A 68, 042320 (2003)

    Article  ADS  Google Scholar 

  21. Deng, Z.J., Feng, M., Gao, K.L.: Preparation of entangled states of four remote atomic qubits in decoherence-free subspace. Phys. Rev. A 75, 024302 (2007)

    Article  ADS  Google Scholar 

  22. Deng, F.G.: One-step error correction for multipartite polarization entanglement. Phys. Rev. A 83, 062316 (2011)

    Article  ADS  Google Scholar 

  23. Sheng, Y.B., Deng, F.G., Zhou, H.Y.: Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity. Phys. Rev. A 77, 042308 (2008)

    Article  ADS  Google Scholar 

  24. Xu, Q., Hu, X.M.: Separated atomic ensembles: multimode squeezed states and multipartite entangled states. Phys. Rev. A 86, 032337 (2012)

    Article  ADS  Google Scholar 

  25. Sheng, Y.B., Deng, F.G.: Efficient quantum entanglement distribution over an arbitrary collective-noise channel. Phys. Rev. A 81, 042332 (2010)

    Article  ADS  Google Scholar 

  26. Pan, J.W., Zeilinger, A.: Greenberger–Horne–Zeilinger-state analyzer. Phys. Rev. A 57, 2208 (1998)

    Article  MathSciNet  ADS  Google Scholar 

  27. Qian, J., Feng, X.L., Gong, S.Q.: Universal Greenberger–Horne–Zeilinger-state analyzer based on two-photon polarization parity detection. Phys. Rev. A 72, 052308 (2005)

    Article  ADS  Google Scholar 

  28. Mower, J., Zhang, Z.S., Desjardins, P., Lee, C., Shapiro, J.H., Englund, D.: High-dimensional quantum key distribution using dispersive optics. Phys. Rev. A 87, 062322 (2013)

    Article  ADS  Google Scholar 

  29. Rousseaux, B., Gurin, S., Vitanov, N.V.: Arbitrary qudit gates by adiabatic passage. Phys. Rev. A 87, 032328 (2013)

    Article  ADS  Google Scholar 

  30. Mischuck, B., MØlmer, K.: Qudit quantum computation in the Jaynes–Cummings model. Phys. Rev. A 87, 022341 (2013)

    Article  ADS  Google Scholar 

  31. Lin, Q.: Heralded generation of symmetric and asymmetric entangled qudits with weak cross-Kerr nonlinearity. JOSA B 30(3), 576 (2013)

    Article  ADS  Google Scholar 

  32. Ye, X.L., Lin, Q.: Efficient and flexible generation of entangled qudits with cross phase modulation. JOSA B 29(7), 1810 (2012)

    Article  ADS  Google Scholar 

  33. Deng, Z.J., Zhang, X.L., Wei, H., Gao, K.L., Feng, M.: Implementation of a nonlocal N-qubit conditional phase gate by single-photon interference. Phys. Rev. A 76, 044305 (2007)

    Article  ADS  Google Scholar 

  34. Song, J., Xia, Y., Song, H.S.: Quantum nodes for W-state generation in noisy channels. Phys. Rev. A 78, 024302 (2008)

    Article  ADS  Google Scholar 

  35. Duan, L.M., Kimble, H.J.: Scalable photonic quantum computation through cavity-assisted interactions. Phys. Rev. Lett. 92, 127902 (2004)

    Article  ADS  Google Scholar 

  36. Xiao, Y.F., Lin, X.M., Gao, J., Yang, Y., Han, Z.F., Guo, G.C.: Realizing quantum controlled phase flip through cavity QED. Phys. Rev. A 70, 042314 (2004)

    Article  ADS  Google Scholar 

  37. Feng, X.L., Zhang, Z.M., Li, X.D., Gong, S.Q., Xu, Z.Z.: Entangling distant atoms by interference of polarized photons. Phys. Rev. Lett. 90, 217902 (2003)

    Article  ADS  Google Scholar 

  38. Lin, X.M., Zhou, Z.W., Ye, M.Y., Xiao, Y.F., Guo, G.C.: One-step implementation of a multiqubit controlled-phase-flip gate. Phys. Rev. A 73, 012323 (2006)

    Article  ADS  Google Scholar 

  39. Zou, X.B., Zhang, S.L., Li, K., Guo, G.C.: Linear optical implementation of the two-qubit controlled phase gate with conventional photon detectors. Phys. Rev. A 75, 034302 (2007)

    Article  ADS  Google Scholar 

  40. Zou, X.B., Li, K., Guo, G.C.: Linear optical scheme for direct implementation of a nondestructive N-qubit controlled. Phys. Rev. A 74, 044305 (2006)

    Article  ADS  Google Scholar 

  41. Ota, Y., Ashhab, S., Nori, F.: Implementing general measurements on linear optical and solid-state qubits. Phys. Rev. A 85, 043808 (2012)

    Article  ADS  Google Scholar 

  42. Eibl, M., Bourennane, M., Kurtsiefer, C., Weinfurter, H.: Experimental realization of a three-qubit entangled W state. Phys. Rev. Lett. 92, 077901 (2004)

    Article  ADS  Google Scholar 

  43. Mikami, H., Li, Y., Kobayashi, T.: Generation of the four-photon W state and other multiphoton entangled states using parametric down-conversion. Phys. Rev. A 70, 052308 (2004)

    Article  ADS  Google Scholar 

  44. Song, J., Xia, Y., Song, H.S., Guo, J.L., Nie, J.: Quantum computation and entangled-state generation through adiabatic evolution in two distant cavities. EPL 80, 60001 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  45. Xiong, W., Ye, L.: Optimal real state quantum cloning machine in cavity quantum electrodynamics. J. Opt. Soc. Am. B 28, 9 (2001)

    Google Scholar 

  46. Fang, B.L., Wu, T., Ye, L.: Realization of a general quantum cloning machine via cavity-assisted interaction. EPL 97, 60002 (2012)

    Article  ADS  Google Scholar 

  47. Zhen, Y., Hai, Z.W., Juan, H., Liu, Y.: Scheme to implement optimal symmetric \(1\rightarrow 2\) universal quantum telecloning through cavity-assisted interaction. Commun. Theor. Phys. (Beijing, China) 50, 1096 (2008)

    Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant Nos. 11047122 and 11105030, the Natural Science Foundation of Fuzhou University of China under Grant Nos. XRC-0976 and 2010-XQ-28, the SRTP Foundation of Fuzhou University of China under Grant No. 16118, the SRTP Foundation of China under Grant No. 201310386025, the funds from Education Department of Fujian Province of China under Grant Nos. JA11005, JA10009 and JA10039, the National Natural Science Foundation of Fujian Province of China under Grant Nos. 2011J01009 and 2012J01269, and the Foundation of Ministry of Education of China under Grant No. 212085.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yan Xia.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kang, YH., Xia, Y. & Lu, PM. Effective scheme for generation of \(N\)-dimension atomic Greenberger–Horne–Zeilinger states. Quantum Inf Process 13, 1255–1265 (2014). https://doi.org/10.1007/s11128-013-0727-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-013-0727-1

Keywords

Navigation