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A Three-Qubit State Entanglement Concentration Protocol Assisted by Two-Qubit Systems

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Abstract

In this paper we present an entanglement concentration protocol for enhancement of the amount of entanglement maximally in a three qubit non-maximally entangled state. We use a Bell state for this purpose. Here the speciality is that no non-local measurement involving more than one parties is involved in the protocol. It is shown that for obtaining best probability of success a maximally entangled Bell state must be used. The probability of success in our protocol increases with an increase in the amount of entanglement in the assisting Bell state, and is zero when the entanglement vanishes.

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References

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

    MATH  Google Scholar 

  2. Mintert, F., Carvalho, A.R.R., Kuś, M., Buchleitner, A.: Measures and dynamics of entangled states. Phys. Rep. 415, 207–259 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  3. 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  MathSciNet  ADS  MATH  Google Scholar 

  4. Ekert, A.K.: Quantum cryptography based on Bells theorem. Phys. Rev. Lett. 67, 661–663 (1991)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. Bennett, C.H., Brassard, G., Mermin, N.D.: Quantum cryptography without Bells theorem. Phys. Rev. Lett. 68, 557–559 (1992)

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  7. 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  MathSciNet  ADS  MATH  Google Scholar 

  8. 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 

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

    Article  MathSciNet  ADS  Google Scholar 

  10. Lance, A.M., Symul, T., Bowen, W.P., Sanders, B.C., Lam, P.K.: Tripartite quantum state sharing. Phys. Rev. Lett. 92, 177903 (2004)

    Article  ADS  Google Scholar 

  11. 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 

  12. Deng, F.G., Li, X.H., Li, C.Y., Zhou, P., Zhou, H.Y.: Quantum state sharing of an arbitrary two-qubit state with two-photon entanglements and Bell-state measurements. Eur. Phys. J. D 39, 459–464 (2006)

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  14. Yang, C.P., Chu, S.I., Han, S.: Efficient many-party controlled teleportation of multiqubit quantum information via entanglement. Phys. Rev. A 70, 022329 (2004)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. 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 

  18. Wang, C., Deng, F.G., Li, Y.S., Liu, X.S., Long, G.L.: Quantum secure direct communication with high-dimension quantum superdense coding. Phys. Rev. A 71, 044305 (2005)

    Article  ADS  Google Scholar 

  19. Zhang, Q., Li, C., Li, Y., Nie, Y.: Quantum secure direct communication based on four-qubit cluster states. Int. J. Theor. Phys. (2012). doi:10.1007/s10773-012-1294-4

    Google Scholar 

  20. 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 

  21. Bennett, C.H., Brassard, G., Popescu, S., Schumacher, B., Smoin, J.A., Wootters, W.K.: Purification of noisy entanglement and faithful teleportation via noisy channels. Phys. Rev. Lett. 76, 722–725 (1996)

    Article  ADS  Google Scholar 

  22. Pan, J.W., Simon, C., Zellinger, A.: Entanglement purification for quantum communication. Nature (London) 410, 1067–1070 (2001)

    Article  ADS  Google Scholar 

  23. Simon, C., Pan, J.W.: Polarization entanglement purification using spatial entanglement. Phys. Rev. Lett. 89, 257901 (2002)

    Article  ADS  Google Scholar 

  24. 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 

  25. Sheng, Y.B., Deng, F.G.: Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement. Phys. Rev. A 81, 032307 (2010)

    Article  ADS  Google Scholar 

  26. Li, X.H.: Deterministic polarization-entanglement purification using spatial entanglement. Phys. Rev. A 82, 044304 (2010)

    Article  ADS  Google Scholar 

  27. Sheng, Y.B., Deng, F.G.: One-step deterministic polarization entanglement purification using spatial entanglement. Phys. Rev. A 82, 044305 (2010)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  29. 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 

  30. Wang, C., Zhang, Y., Jin, G.S.: Polarization-entanglement purification and concentration using cross-Kerr nonlinearity. Quantum Inf. Comput. 11, 0988–1002 (2011)

    MathSciNet  Google Scholar 

  31. Cao, Zh.L., Yang, M.: Entanglement distillation for three-particle W class states. J. Phys. B 36, 4245–4253 (2003)

    Article  ADS  Google Scholar 

  32. Yang, M., Cao, Z.L.: Entanglement distillation for W class states. Physica A 337, 141–148 (2004)

    Article  ADS  Google Scholar 

  33. Yang, M., Song, W., Cao, Z.L.: Entanglement distillation for atomic states via cavity QED. Physica A 341, 251–261 (2004)

    Article  ADS  Google Scholar 

  34. 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 

  35. 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 

  36. 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 

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

    Article  ADS  Google Scholar 

  38. 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 

  39. Sheng, Y.B., Deng, F.G., Zhou, H.Y.: Efficient polarization entanglement concentration for electron with charge detection. Phys. Lett. A 373, 1823–1825 (2009)

    Article  ADS  MATH  Google Scholar 

  40. 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)

    MathSciNet  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  42. Gu, B., Quan, D.H., Xiao, S.R.: Multi-photon entanglement concentration protocol for partially entangled W states with projection measurement. Int. J. Theor. Phys. 51, 2966–2973 (2012). doi:10.1007/s10773-012-1178-7

    Article  MATH  Google Scholar 

  43. 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 

  44. 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 

  45. Du, F.F., Li, T., Ren, B.C., Wei, H.R., Deng, F.G.: Single-photon-assisted entanglement concentration of a multiphoton 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 

  46. Sheng, Y.B., Zhou, L., Zhao, S.M.: Efficient two-step entanglement concentration for arbitrary W states. Phys. Rev. A 85, 042302 (2012)

    Article  ADS  Google Scholar 

  47. Choudhury, B.S., Dhara, A.: An entanglement concentration protocol for cluster states. Quantum Inf. Process. 12, 2577–2585 (2013). doi:10.1007/s11128-013-0549-1

    Article  MathSciNet  ADS  MATH  Google Scholar 

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Acknowledgements

This work is supported by the University Grants Commission of India. The support is gratefully acknowledged. The authors gratefully acknowledge the valuable suggestions made by the referee.

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Authors and Affiliations

  1. Department of Mathematics, Bengal Engineering and Science University, Shibpur, B. Garden, Shibpur, Howrah, 711103, West Bengal, INDIA

    Binayak S. Choudhury & Arpan Dhara

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  1. Binayak S. Choudhury
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  2. Arpan Dhara
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Correspondence to Arpan Dhara.

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Choudhury, B.S., Dhara, A. A Three-Qubit State Entanglement Concentration Protocol Assisted by Two-Qubit Systems. Int J Theor Phys 52, 3965–3969 (2013). https://doi.org/10.1007/s10773-013-1709-x

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  • DOI: https://doi.org/10.1007/s10773-013-1709-x

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