Skip to main content
Log in

Efficient Entanglement Concentration for Arbitrary Less-Entangled N-Atom GHZ State

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

In this paper, we put forward an effective ECP for arbitrary less-entangled N-atom GHZ state with the help of the photonic Faraday rotation. In our protocol, we only require one pair of less-entangled atom state, one auxiliary atom and one auxiliary photon, and can complete the concentration task with relatively high success probability. Moreover, our ECP can be used repeatedly to further increase the success probability. Especially, if consider the practical operation and imperfect detection, our protocol is more efficient. This ECP may be useful in current quantum information processing.

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.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777–780 (1935)

    Article  ADS  MATH  Google Scholar 

  2. Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74, 145–195 (2002)

    Article  ADS  Google Scholar 

  3. Long, G.L., Xiao, L.: Parallel quantum computing in a single ensemble quantum computer. Phys. Rev. A 69, 052303 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  4. Feng, G.R., Xu, G.F., Long, G.L.: Experimental realization of nonadiabatic holonomic quantum computation. Phys. Rev. Lett. 110, 190501 (2013)

    Article  ADS  Google Scholar 

  5. Wei, H.R., Deng, F.G.: Universal quantum gates for hybrid systems assisted by quantum dots inside double-sided optical microcavities. Phys. Rev. A 87, 022305 (2013)

    Article  ADS  Google Scholar 

  6. Wei, H.R., Deng, F.G.: Scalable photonic quantum computing assisted by quantum-dot spin in double-sided optical microcavity. Opt. Express 21, 17671–17685 (2013)

    Article  ADS  Google Scholar 

  7. Ren, B.C., Wei, H.R., Deng, F.G.: Deterministic photonic spatial-polarization hyper-controlled-not gate assisted by a quantum dot inside a one-side optical microcavity. Laser Phys. Lett. 10, 095202 (2013)

    Article  ADS  Google Scholar 

  8. Guo, Y., Hou, J.C.: Entanglement detection beyond the CCNR criterionfor infinite-dimensions. Chin. Sci. Bull. (2013). doi:10.1007/s11434-013-5738-x

    Google Scholar 

  9. Man, Z.X., Su, F., Xia, Y.J.: Stationary entanglement of two atoms in a common reservoir. Chin. Sci. Bull. 58, 2423–2429 (2013)

    Article  Google Scholar 

  10. Yu, X.Y., Li, J.H., Li, X.B.: Atom-atom entanglement characteristics in fiber-connected cavities system within the double-excitation space. Sci. China, Phys. Mech. Astron. 55, 1813–1819 (2012)

    Article  ADS  Google Scholar 

  11. Wang, C., Sheng, Y.B., Li, X.H., Deng, F.G., Zhang, W., Long, G.L.: Efficient entanglement purification for doubly entangled photon state. Sci. China, Technol. Sci. 52, 3464–3467 (2009)

    Article  MATH  Google Scholar 

  12. 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, 1895–1899 (1993)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  13. Karlsson, A., Bourennane, M.: Quantum teleportation using three-particle entanglement. Phys. Rev. A 58, 4394–4400 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  14. Deng, F.G., Li, C.Y., Li, Y.S., Zhou, H.Y., Wang, Y.: Symmetric multiparty-controlled teleportation of an arbitrary two-particle entanglement. Phys. Rev. A 72, 022338 (2005)

    Article  ADS  Google Scholar 

  15. Bennett, C.H., Wiesner, S.J.: Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett. 69, 2881–2884 (1992)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  16. Hillery, M., Buz̃ek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829–1834 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  17. Karlsson, A., Koashi, M., Imoto, N.: Quantum entanglement for secret sharing and secret splitting. Phys. Rev. A 59, 162–168 (1999)

    Article  ADS  Google Scholar 

  18. Xiao, L., Long, G.L., Deng, F.G., Pan, J.W.: Efficient multiparty quantum-secret-sharing schemes. Phys. Rev. A 69, 052307 (2004)

    Article  ADS  Google Scholar 

  19. Deng, F.G., Li, X.H., Li, C.Y., Zhou, P., Zhou, H.Y.: Multiparty quantum-state sharing of an arbitrary two-particle state with Einstein-Podolsky-Rosen pairs. Phys. Rev. A 72, 044301 (2005)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  21. Long, G.L., Liu, X.S.: Theoretically efficient high-capacity quantum-key-distribution scheme. Phys. Rev. A 65, 032302 (2002)

    Article  ADS  Google Scholar 

  22. Wang, C., Deng, F.G., Li, Y.S., Liu, X.S., Long, G.L.: Robustness of differential-phase-shift quantum key distribution against photon-number-splitting attack. Phys. Rev. A 71, 044305 (2005)

    Article  ADS  Google Scholar 

  23. Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661–663 (1991)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  24. Deng, F.G., Long, G.L.: Controlled order rearrangement encryption for quantum ey distribution. Phys. Rev. A 68, 042315 (2003)

    Article  ADS  Google Scholar 

  25. Li, X.H., Deng, F.G., Zhou, H.Y.: Efficient quantum key distribution over a collective noise channel. Phys. Rev. A 78, 022321 (2008)

    Article  ADS  Google Scholar 

  26. Duan, L.M., Lukin, M.D., Cirac, J.I., Zoller, P.: Long-distance quantum communication with atomic ensembles and linear optics. Nature 414, 413–418 (2001)

    Article  ADS  Google Scholar 

  27. Bennett, C.H., Bernstein, H.J., Popescu, S., Schumacher, B.: Concentrating partial entanglement by local operations. Phys. Rev. A 53, 2046–2052 (1996)

    Article  ADS  Google Scholar 

  28. Bose, S., Vedral, V., Knight, P.L.: Purification via entanglement swapping and conserved entanglement. Phys. Rev. A 60, 194–197 (1999)

    Article  ADS  Google Scholar 

  29. Shi, B.S., Jiang, Y.K., Guo, G.C.: Optimal entanglement purification via entanglement swapping. Phys. Rev. A 62, 054301 (2000)

    Article  ADS  Google Scholar 

  30. Zhao, Z., Pan, J.W., Zhan, M.S.: Practical scheme for entanglement concentration. Phys. Rev. A 64, 014301 (2001)

    Article  ADS  Google Scholar 

  31. Yamamoto, T., Koashi, M., Imoto, N.: Concentration and purification scheme for two partially entangled photon pairs. Phys. Rev. A 64, 012304 (2001)

    Article  ADS  Google Scholar 

  32. Sheng, Y.B., Deng, F.G., Zhou, H.Y.: Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics. Phys. Rev. A 77, 062325 (2008)

    Article  ADS  Google Scholar 

  33. Sheng, Y.B., Zhou, L., Zhao, S.M., Zheng, B.Y.: Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs. Phys. Rev. A 85, 012307 (2012)

    Article  ADS  Google Scholar 

  34. Sheng, Y.B., Zhou, L., Zhao, S.M.: Efficient two-step entanglement concentration for arbitrary W-states. Phys. Rev. A 85, 044305 (2012)

    Google Scholar 

  35. Sheng, Y.B., Deng, F.G., Zhou, H.Y.: Single-photon entanglement concentration for long-distance quantum communication. Quantum Inf. Comput. 10, 272–281 (2010)

    MATH  MathSciNet  Google Scholar 

  36. Deng, F.G.: Optimal nonlocal multipartite entanglement concentration based on projection measurements. Phys. Rev. A 85, 022311 (2012)

    Article  ADS  Google Scholar 

  37. Ren, B.C., Du, F.F., Deng, F.G.: Hyperentanglement concentration for two-photon four-qubit systems with linear optics. Phys. Rev. A 88, 012302 (2013)

    Article  ADS  Google Scholar 

  38. Sheng, Y.B., Zhou, L., Wang, L., Zhao, S.M.: Efficient entanglement concentration for quantum dot and optical microcavities systems. Quantum Inf. Process. 12, 1885–1895 (2013)

    Article  ADS  MATH  Google Scholar 

  39. Sheng, Y.B., Zhou, L.: Efficient W-state entanglement concentration using quantum-dot and optical microcavities. J. Opt. Soc. Am. B 30, 678–686 (2012)

    Article  ADS  Google Scholar 

  40. Zhou, L., Sheng, Y.B., Cheng, W.W., Gong, L.Y., Zhao, S.M.: Efficient entanglement concentration for arbitrary single-photon multimode W-state. J. Opt. Soc. Am. B 30, 71–78 (2013)

    Article  ADS  Google Scholar 

  41. Zhou, L.: Efficient entanglement concentration for electron-spin W-state with the charge detection. Quantum Inf. Process. 12, 2087–2101 (2013)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  42. Sheng, Y.B., Zhou, L.: Quantum entanglement concentration for quantum communications. Entropy 15, 1776–1820 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  43. Gu, B.: Single-photon-assisted entanglement concentration of partially entangled multiphoton W-states with linear optics. J. Opt. Soc. Am. B 29, 1685–1689 (2012)

    Article  ADS  Google Scholar 

  44. Du, F.F., Li, T., Ren, B.C., Wei, H.R., Deng, F.G.: Single-photon-assisted entanglement concentration of a multi-photon system in a partially entangled W-state with weak cross-Kerr nonlinearity. J. Opt. Soc. Am. B 29, 1399–1405 (2012)

    Article  ADS  Google Scholar 

  45. Wang, C., Zhang, Y., Jin, G.S.: Entanglement purification and concentration of electron-spin entangled states using quantum-dot spins in optical microcavities. Phys. Rev. A 84, 032307 (2011)

    Article  ADS  Google Scholar 

  46. Wang, C.: Efficient entanglement concentration for partially entangled electrons using a quantum-dot and microcavity coupled system. Phys. Rev. A 86, 012323 (2012)

    Article  ADS  Google Scholar 

  47. Wang, C., Zhang, Y., Jin, G.S., Zhang, R.: Efficient entanglement purification of separate nitrogen-vacancy centers via coupling to microtoroidal resonators. J. Opt. Soc. Am. B 29, 3349–3354 (2012)

    Article  ADS  Google Scholar 

  48. Peng, Z.H., Zou, J., Liu, X.J., Xiao, Y.J., Kuang, L.M.: Atomic and photonic entanglement concentration via photonic Faraday rotation. Phys. Rev. A 86, 034305 (2012)

    Article  ADS  Google Scholar 

  49. Cirac, J.I., Zoller, P., Kimble, H.J., Mabuchi, H.: Quantum state transfer and entanglement distribution among distant nodes in a quantum network. Phys. Rev. Lett. 78, 3221–3224 (1997)

    Article  ADS  Google Scholar 

  50. Cirac, J.I., Ekert, A.K., Huelga, S.F., Macchiavello, C.: Distributed quantum computation over noisy channels. Phys. Rev. A 59, 4249–4254 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  51. Turchette, Q.A., Hood, C.J., Lange, W., Mabuchi, H., Kimble, H.J.: Measurement of conditional phase shifts for quantum logic. Phys. Rev. Lett. 75, 4710–4713 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  52. Mattle, K., Weinfurter, H., Kwiat, P.G., Zeilinger, A.: Dense coding in experimental quantum communication. Phys. Rev. Lett. 76, 4656–4659 (1996)

    Article  ADS  Google Scholar 

  53. Xue, P., Xiao, Y.F.: Universal quantum computation in decoherence-free subspace with neutral atoms. Phys. Rev. Lett. 97, 140501 (2006)

    Article  ADS  Google Scholar 

  54. 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 

  55. Cho, J., Lee, H.W.: Generation of atomic cluster states through the cavity input-output process. Phys. Rev. Lett. 95, 160501 (2005)

    Article  ADS  Google Scholar 

  56. Duan, L.M., Wang, B., Kimble, H.J.: Robust quantum gates on neutral atoms with cavity-assisted photon scattering. Phys. Rev. A 72, 032333 (2005)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  58. 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 

  59. 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 

  60. Wei, H., Deng, Z.J., Zhang, X.L., Feng, M.: Transfer and teleportation of quantum states encoded in decoherence-free subspace. Phys. Rev. A 76, 054304 (2007)

    Article  ADS  Google Scholar 

  61. Dayan, B., Parkins, A.S., Aoki, T., Ostby, E.P., Vahala, K.I., Kimble, H.J.: A photon turnstile dynamically regulated by one atom. Science 319, 1062–1065 (2008)

    Article  ADS  Google Scholar 

  62. An, J.H., Feng, M., Oh, C.H.: Quantum-information processing with a single photon by an input-output process with respect to low-Q cavities. Phys. Rev. A 79, 032303 (2009)

    Article  ADS  Google Scholar 

  63. Chen, Q., Feng, M.: Quantum-information processing in decoherence-free subspace with low-Q cavities. Phys. Rev. A 82, 052329 (2010)

    Article  ADS  Google Scholar 

  64. Chen, J.J., An, J.H., Feng, M., Liu, G.: Teleportation of an arbitrary multipartite state via photonic Faraday rotation. J. Phys. B 43, 095505 (2010)

    Article  ADS  Google Scholar 

  65. Bastos, W.P., Cardoso, W.B., Avelar, A.T., de Almeida, N.G., Baseia, B.: Controlled teleportation via photonic Faraday rotations in low-Q cavities. Quantum Inf. Process. 11, 1867–1881 (2012)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  66. Mei, F., Yu, Y.F., Feng, X.L., Zhang, Z.M., Oh, C.H.: Quantum entanglement distribution with hybrid parity gate. Phys. Rev. A 82, 052315 (2010)

    Article  ADS  Google Scholar 

  67. Bastos, W.P., Cardoso, W.B., Avelar, A.T., Baseia, B.: A note on entanglement swapping of atomic states through the photonic Faraday rotation. Quantum Inf. Process. 10, 395–404 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  68. Julsgaard, B., Kozhekin, A., Polzik, E.S.: Experimental long-lived entanglement of two macroscopic objects. Nature (London) 413, 400 (2001)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant Nos. 11104159, 11347110, the Scientific Research Foundation of Nanjing University of Posts and Telecommunications (Grant No. NY213054), and the Priority Academic Program Development of Jiangsu Higher Education Institutions.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yu-Bo Sheng.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhou, L., Wang, XF. & Sheng, YB. Efficient Entanglement Concentration for Arbitrary Less-Entangled N-Atom GHZ State. Int J Theor Phys 53, 1752–1766 (2014). https://doi.org/10.1007/s10773-013-1974-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-013-1974-8

Keywords

Navigation