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Quantum Information Processing

, Volume 13, Issue 6, pp 1397–1412 | Cite as

Efficient entanglement purification via quantum communication bus

  • Meng-Zheng Zhu
  • Liu Ye
Article

Abstract

A scheme is proposed to implement entanglement purification for two remote less entangled photons using robust continuous variable coherent modes, called as quantum communication bus (qubus), rather than consuming expensive ancilla single-photon sources. The qubus beams in the coherent states provide for the natural communication in the purification protocol, instead of the classical communication between the distant photons. Weak cross-Kerr nonlinearities, qubus beams and quantum non-demolition (QND) photon-number-resolving measurement are utilized for implementing deterministic entanglement purification. The core element to realize the QND measurement is Kerr nonlinearity. The necessary QND measurement in the present scheme is not an extra, very difficult, addition to the present protocol, but is taken care of by a phase measurement. The entanglement purification protocol (EPP) can obtain a maximally entangled pair with only one step, instead of improving the fidelity of less entangled pairs by performing continuous indefinite iterative purification procedure. The total success probability and fidelity of the present purification scheme can approach unit in principle. In addition, we investigate photon loss of the qubus beams during the transmission and decoherence effects in the entanglement purification caused by such a photon loss.

Keywords

Quantum communications Entanglement Entanglement purification 

Notes

Acknowledgments

This work was supported by the National Science Foundation of China under Grant No. 11074002 and No. 61275119 and also the Doctoral Foundation of the Ministry of Education of China under Grant No. 20103401110003.

References

  1. 1.
    Horodecki, R., Horodecki, P.L., Horodecki, M.L., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865–942 (2009)MathSciNetCrossRefADSzbMATHGoogle Scholar
  2. 2.
    Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661–663 (1991)MathSciNetCrossRefADSzbMATHGoogle Scholar
  3. 3.
    Bennett, C.H., Brassard, G., Cr Epeau, 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)Google Scholar
  4. 4.
    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)MathSciNetCrossRefADSzbMATHGoogle Scholar
  5. 5.
    Bennett, C.H., Brassard, G., Popescu, S., Schumacher, B., Smolin, J.A., Wootters, W.K.: Purification of noisy entanglement and faithful teleportation via noisy channels. Phys. Rev. Lett. 76, 722–725 (1996)CrossRefADSGoogle Scholar
  6. 6.
    Briegel, H.J., Dür, W., Cirac, J.I., Zoller, P.: Quantum repeaters: the role of imperfect local operations in quantum communication. Phys. Rev. Lett. 81, 5932–5935 (1998)Google Scholar
  7. 7.
    Deutsch, D., Ekert, A., Jozsa, R., Macchiavello, C., Popescu, S., Sanpera, A.: Quantum privacy amplification and the security of quantum cryptography over noisy channels. Phys. Rev. Lett. 77, 2818–2821 (1996)CrossRefADSGoogle Scholar
  8. 8.
    Pan, J., Simon, C., Brukner, C., Zeilinger, A.: Entanglement purification for quantum communication. Nature 410, 1067–1070 (2001)CrossRefADSGoogle Scholar
  9. 9.
    Pan, J., Gasparoni, S., Ursin, R., Weihs, G., Zeilinger, A.: Experimental entanglement purification of arbitrary unknown states. Nature 423, 417–422 (2003)CrossRefADSGoogle Scholar
  10. 10.
    Deng, F.: Optimal nonlocal multipartite entanglement concentration based on projection measurements. Phys. Rev. A 85, 022311 (2012)CrossRefADSGoogle Scholar
  11. 11.
    Bose, S., Vedral, V., Knight, P.L.: Purification via entanglement swapping and conserved entanglement. Phys. Rev. A 60, 194–197 (1999)CrossRefADSGoogle Scholar
  12. 12.
    Sangouard, N., Simon, C., Coudreau, T., Gisin, N.: Purification of single-photon entanglement with linear optics. Phys. Rev. A 78, 050301 (2008)CrossRefADSGoogle Scholar
  13. 13.
    Shi, B., Jiang, Y., Guo, G.: Optimal entanglement purification via entanglement swapping. Phys. Rev. A 62, 054301 (2000)CrossRefADSGoogle Scholar
  14. 14.
    Yamamoto, T., Koashi, M., Imoto, N.: Concentration and purification scheme for two partially entangled photon pairs. Phys. Rev. A 64, 012304 (2001)CrossRefADSGoogle Scholar
  15. 15.
    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)CrossRefADSGoogle Scholar
  16. 16.
    Zhao, Z., Pan, J., Zhan, M.S.: Practical scheme for entanglement concentration. Phys. Rev. A 64, 014301 (2001)CrossRefADSGoogle Scholar
  17. 17.
    Simon, C., Pan, J.: Polarization entanglement purification using spatial entanglement. Phys. Rev. Lett. 89, 257901 (2002)CrossRefADSGoogle Scholar
  18. 18.
    Sheng, Y., Deng, F.: One-step deterministic polarization-entanglement purification using spatial entanglement. Phys. Rev. A 82, 044305 (2010)CrossRefADSGoogle Scholar
  19. 19.
    Li, X.: Deterministic polarization-entanglement purification using spatial entanglement. Phys. Rev. A 82, 044304 (2010)CrossRefADSGoogle Scholar
  20. 20.
    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)CrossRefADSGoogle Scholar
  21. 21.
    Sheng, Y., Deng, F.: Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement. Phys. Rev. A 81, 032307 (2010)CrossRefADSGoogle Scholar
  22. 22.
    Sheng, Y., Zhou, L., Zhao, S., Zheng, B.: Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs. Phys. Rev. A 85, 012307 (2012)CrossRefADSGoogle Scholar
  23. 23.
    Sheng, Y., Zhou, L., Zhao, S.: Efficient two-step entanglement concentration for arbitrary W states. Phys. Rev. A 85, 042302 (2012)CrossRefADSGoogle Scholar
  24. 24.
    Song, X., Feng, X., Kwek, L.C., Oh, C.H.: Entanglement purification based on photonic polarization parity measurements. J. Phys. B: At. Mol. Opt. Phys. 38, 2827–2832 (2005)CrossRefADSGoogle Scholar
  25. 25.
    Kok, P., Lovett, B.: Introduction to Optical Quantum Information Processing. Cambridge University Press, Cambridge (2010)CrossRefzbMATHGoogle Scholar
  26. 26.
    Milburn, G.J.: Quantum optical Fredkin gate. Phys. Rev. Lett. 62, 2124–2127 (1989)CrossRefADSGoogle Scholar
  27. 27.
    Munro, W.J., Nemoto, K., Spiller, T.P.: Weak nonlinearities: a new route to optical quantum computation. New J. Phys. 7, 137 (2005)CrossRefADSGoogle Scholar
  28. 28.
    Imoto, N., Haus, H.A., Yamamoto, Y.: Quantum nondemolition measurement of the photon number via the optical Kerr effect. Phys. Rev. A 32, 2287–2292 (1985)CrossRefADSGoogle Scholar
  29. 29.
    Louis, S.G.R., Nemoto, K., Munro, W.J., Spiller, T.P.: The efficiencies of generating cluster states with weak nonlinearities. New J. Phys. 9, 193 (2007)CrossRefADSGoogle Scholar
  30. 30.
    Zhao, C.R., Ye, L.: Robust scheme for the preparation of symmetric Dicke states with coherence state via cross-Kerr nonlinearity. Opt. Commun. 284, 541–544 (2011)CrossRefADSGoogle Scholar
  31. 31.
    Nemoto, K., Munro, W.J.: Nearly deterministic linear optical controlled-NOT gate. Phys. Rev. Lett. 93, 250502 (2004)CrossRefADSGoogle Scholar
  32. 32.
    He, B., Nadeem, M., Bergou, J.A.A.: Scheme for generating coherent-state superpositions with realistic cross-Kerr nonlinearity. Phys. Rev. A 79, 035802 (2009)CrossRefADSGoogle Scholar
  33. 33.
    Bachor, H., Ralph, T.C.: A Guide to Experiments in Quantum Optics. Wiley-VCH, Weinheim (2004)CrossRefGoogle Scholar
  34. 34.
    Zhu, M.Z., Yin, X.G.: Highly efficient optical Fredkin gate with weak nonlinearities and classical information feed-forward. J. Opt. Soc. Am. B 30, 355–361 (2013)CrossRefADSGoogle Scholar
  35. 35.
    Gerry, C.C., Bui, T.: Quantum non-demolition measurement of photon number using weak nonlinearities. Phys. Lett. A 372, 7101–7104 (2008)CrossRefADSzbMATHGoogle Scholar
  36. 36.
    Jiang, L.A., Dauler, E.A., Chang, J.T.: Photon-number-resolving detector with 10 bits of resolution. Phys. Rev. A 75, 062325 (2007)CrossRefADSGoogle Scholar
  37. 37.
    Achilles, D., Silberhorn, C., Sliwa, C., Banaszek, K., Walmsley, I.A., Fitch, M.J., Jacobs, B.C., Pittman, T.B., Franson, J.D.: Photon-number-resolving detection using time-multiplexing. J. Mod. Opt. 51, 1499–1515 (2004)CrossRefADSzbMATHGoogle Scholar
  38. 38.
    Lin, Q., He, B., Bergou, J.A., Ren, Y.: Processing multiphoton states through operation on a single photon: methods and applications. Phys. Rev. A 80, 042311 (2009)CrossRefADSGoogle Scholar
  39. 39.
    Spiller, T.P., Nemoto, K., Braunstein, S.L., Munro, W.J., van Loock, P., Milburn, G.J.: Quantum computation by communication. New J. Phys. 8, 30 (2006)CrossRefADSGoogle Scholar
  40. 40.
    Munro, W.J., Nemoto, K., Spiller, T.P., Barrett, S.D., Kok, P., Beausoleil, R.G.: Efficient optical quantum information processing. J. Opt. B: Quantum Semiclass. Opt. 7, S135–S140 (2005)CrossRefADSGoogle Scholar
  41. 41.
    Jeong, H.: Quantum computation using weak nonlinearities: robustness against decoherence. Phys. Rev. A 73, 052320 (2006)CrossRefADSGoogle Scholar
  42. 42.
    Yamamoto, T., Hayashi, K., Ozdemir, S.K., Koashi, M., Imoto, N.: Robust photonic entanglement distribution by state-independent encoding onto decoherence-free subspace. Nat. Photon 2, 488–491 (2008)CrossRefGoogle Scholar
  43. 43.
    Phoenix, S.J.D.: Wave-packet evolution in the damped oscillator. Phys. Rev. A 41, 5132–5138 (1990)MathSciNetCrossRefADSGoogle Scholar
  44. 44.
    Rohde, P.P., Munro, W.J., Ralph, T.C., van Loock, P., Nemoto, K.: Practical effects in the preparation of cluster states using weak non-linearities. Quantum Inf. Comput. 8, 53–67 (2008)MathSciNetzbMATHGoogle Scholar
  45. 45.
    van Enk, S.J., Hirota, O.: Entangled coherent states: teleportation and decoherence. Phys. Rev. A 64, 022313 (2001)CrossRefADSGoogle Scholar
  46. 46.
    He, B., Ren, Y.H., Bergou, J.A.: Creation of high-quality long-distance entanglement with flexible resources. Phys. Rev. A 79, 052323 (2009)CrossRefADSGoogle Scholar
  47. 47.
    Fleischhauer, M., Imamoglu, A., Marangos, J.P.: Electromagnetically induced transparency: optics in coherent media. Rev. Mod. Phys. 77, 633–673 (2005)CrossRefADSGoogle Scholar
  48. 48.
    Friedler, I., Petrosyan, D., Fleischhauer, M., Kurizki, G.: Long-range interactions and entanglement of slow single-photon pulses. Phys. Rev. A 72, 043803 (2005)CrossRefADSGoogle Scholar
  49. 49.
    He, B., MacRae, A., Han, Y., Lvovsky, A.I., Simon, C.: Transverse multimode effects on the performance of photon-photon gates. Phys. Rev. A 83, 022312 (2011)CrossRefADSGoogle Scholar
  50. 50.
    He, B., Lin, Q., Simon, C.: Cross-Kerr nonlinearity between continuous-mode coherent states and single photons. Phys. Rev. A 83, 053826 (2011)CrossRefADSGoogle Scholar
  51. 51.
    He, B., Scherer, A.: Continuous-mode effects and photon-photon phase gate performance. Phys. Rev. A 85, 033814 (2012)CrossRefADSGoogle Scholar
  52. 52.
    Gea-Banacloche, J.: Impossibility of large phase shifts via the giant Kerr effect with single-photon wave packets. Phys. Rev. A 81, 043823 (2010)CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.School of Physics and Material ScienceAnhui UniversityHefeiChina
  2. 2.School of Physics and Electronic InformationHuaibei Normal UniversityHuaibeiChina

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