OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry van Driel
  • Vol. 28, Iss. 8 — Aug. 1, 2011
  • pp: 2030–2037

Schemes for entanglement concentration of two unknown partially entangled states with cross-Kerr nonlinearity

Wei Xiong and Liu Ye  »View Author Affiliations

JOSA B, Vol. 28, Issue 8, pp. 2030-2037 (2011)

View Full Text Article

Enhanced HTML    Acrobat PDF (749 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We propose practical schemes for concentrating entanglement of a pair of unknown partially entangled Bell states and three-photon W states with cross-Kerr nonlinearity. In these schemes, utilizing local operations and classical communication, two separated parties can obtain one maximally entangled photon pair from two previously shared partially entangled photon pairs, and three separated parties can obtain one maximally entangled three-photon W state and a maximally entangled cluster state from two identical partially entangled three-photon W states with a certain success probability. Finally, we discuss the influence of sources of error and decoherence on the schemes. The proposed setup only employs some linear optical elements and the cross-Kerr medium, which greatly reduces the difficulty of experimental realization. These schemes are feasible with current experimental technology.

© 2011 Optical Society of America

OCIS Codes
(190.1900) Nonlinear optics : Diagnostic applications of nonlinear optics
(190.3270) Nonlinear optics : Kerr effect
(190.4370) Nonlinear optics : Nonlinear optics, fibers
(270.4180) Quantum optics : Multiphoton processes
(270.5565) Quantum optics : Quantum communications
(270.5585) Quantum optics : Quantum information and processing

ToC Category:
Quantum Optics

Original Manuscript: March 30, 2011
Revised Manuscript: June 10, 2011
Manuscript Accepted: June 11, 2011
Published: July 27, 2011

Wei Xiong and Liu Ye, "Schemes for entanglement concentration of two unknown partially entangled states with cross-Kerr nonlinearity," J. Opt. Soc. Am. B 28, 2030-2037 (2011)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993). [CrossRef] [PubMed]
  2. D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997). [CrossRef]
  3. A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998). [CrossRef] [PubMed]
  4. A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991). [CrossRef] [PubMed]
  5. T. Jennewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett. 84, 4729–4732 (2000). [CrossRef] [PubMed]
  6. D. S. Naik, C. G. Peterson, A. G. White, A. J. Berglund, and P. G. Kwiat, “Entangled state quantum cryptography: eavesdropping on the Ekert protocol,” Phys. Rev. Lett. 84, 4733–4736 (2000). [CrossRef] [PubMed]
  7. W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84, 4737–4740 (2000). [CrossRef] [PubMed]
  8. L. K. Grover, “Quantum mechanics helps in searching for a needle in a haystack,” Phys. Rev. Lett. 79, 325–328 (1997). [CrossRef]
  9. C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69, 2881–2884 (1992). [CrossRef] [PubMed]
  10. C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett. 68, 3121–3124 (1992). [CrossRef] [PubMed]
  11. C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046–2052 (1996). [CrossRef] [PubMed]
  12. C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722–725 (1996). [CrossRef] [PubMed]
  13. M. Murao, M. B. Plenio, S. Popescu, V. Vedral, and P. L. Knight, “Multiparticle entanglement purification protocols,” Phys. Rev. A 57, R4075–R4078 (1998). [CrossRef]
  14. S. Parker, S. Bose, and M. B. Plenio, “Entanglement quantification and purification in continuous-variable systems,” Phys. Rev. A 61, 032305 (2000). [CrossRef]
  15. L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Entanglement purification of gaussian continuous variable quantum states,” Phys. Rev. Lett. 84, 4002–4005 (2000). [CrossRef] [PubMed]
  16. F. Morikoshi, “Recovery ofentanglement lost in entanglement manipulation,” Phys. Rev. Lett. 84, 3189–3192 (2000). [CrossRef] [PubMed]
  17. Z. Zhao, J. W. Pan, and M. S. Zhan, “Practical scheme for entanglement concentration,” Phys. Rev. A 64, 014301 (2001). [CrossRef]
  18. C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, “Mixed-state entanglement and quantum error correction,” Phys. Rev. A 54, 3824–3851 (1996). [CrossRef] [PubMed]
  19. H. K. Lo and S. Popescu, “Beyond mean values concentrating entanglement by local actions,” Phys. Rev. A 63, 022301 (2001). [CrossRef]
  20. S. Bose, V. Vedral, and P. L. Knight, “Purification via entanglement swapping and conserved entanglement,” Phys. Rev. A 60, 194–197 (1999). [CrossRef]
  21. T. Yamamoto, M. Koashi, and N. Imoto, “Concentration and purification scheme for two partially entangled photon pairs,” Phys. Rev. A 64, 012304 (2001). [CrossRef]
  22. M. Yang, Y. Zhao, W. Song, and Z. L. Cao, “Entanglement concentration for unknown atomic entangled states via entanglement swapping,” Phys. Rev. A 71, 044302 (2005). [CrossRef]
  23. Z. L. Cao, L. H. Zhang, and M. Yang, “Concentration for unknown atomic entangled states via cavity decay,” Phys. Rev. A 73, 014303 (2006). [CrossRef]
  24. D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 77, 2818–2821 (1996). [CrossRef] [PubMed]
  25. J. W. Pan, C. Simon, C. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature 410, 1067–1070 (2001). [CrossRef] [PubMed]
  26. Z. Zhao, T. Yang, Y. A. Chen, A. N. Zhang, and J. W. Pan, “Experimental realization of entanglement concentration and a quantum repeater,” Phys. Rev. Lett. 90, 207901 (2003). [CrossRef] [PubMed]
  27. T. Yamomoto, M. Koashi, S. K. Ozdemir, and N. Imoto, “Experimental extraction of an entangled photon pair from two identically decohered pairs,” Nature 421, 343–346 (2003). [CrossRef]
  28. H. F. Wang, S. Zhang, and K. H. Yeon, “Linear-optics-based entanglement concentration of unknown partially entangled three-photon W states,” J. Opt. Soc. Am. B 27, 2159–2164 (2010). [CrossRef]
  29. J. Tan, X. W. Wang, and M. F. Fang, “Generation and concentration of multi-atom entangled states,” J. Phys. B 39, 741–748(2006). [CrossRef]
  30. K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502(2004). [CrossRef]
  31. G. J. Milburn and D. F. Walls, “State reduction in quantum-counting quantum nondemolition measurements,” Phys. Rev. A 30, 56–60 (1984). [CrossRef]
  32. R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Phys. Rev. Lett. 86, 5188–5191 (2001). [CrossRef] [PubMed]
  33. S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302(R) (2005). [CrossRef]
  34. T. P. Spiller, K. Nemoto, S. L. Braunstein, W. J. Munro, P. V. Loock, and G. J. Milburn, “Quantum computation by communication,” New J. Phys. 8, 30–55 (2006). [CrossRef]
  35. Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics,” Phys. Rev. A 77, 062325(2008). [CrossRef]
  36. H. F. Wang, S. Zhang, and K. H. Yeon, “Linear optical scheme for entanglement concentration of two partially entangled three-photon W states,” Eur. Phys. J. D 56, 271–275 (2010). [CrossRef]
  37. W. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137–149 (2005). [CrossRef]
  38. Hyunseok Jeong, “Quantum computation using weak nonlinearities: robustness against decoherence,” Phys. Rev. A 73, 052320(2006). [CrossRef]
  39. S. D. Barrett and G. J. Milburn, “Quantum-information processing via a lossy bus,” Phys. Rev. A 74, 060302(R) (2006). [CrossRef]
  40. H. J. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Phys. 9, 16–33(2007). [CrossRef]
  41. N. Matsuda, R. Shimizu, Y. Mitsumori, H. Kosaka, A. Sato, H. Yokoyama, K. Yamada, T. Watanabe, T. Tsuchizawa, H. Fukuda, S. Itabashi, and K. Edamatsu, “All-optical phase modulations in a silicon wire waveguide at ultralow light levels,” Appl. Phys. Lett. 95, 171110 (2009). [CrossRef]
  42. N. Imoto, H. A. Haus, and Y. Yamamoto, “Quantum nondemolition measurement of the photon number via the optical Kerr effect,” Phys. Rev. A 32, 2287–2292 (1985). [CrossRef] [PubMed]
  43. X. M. Lin, Z. W. Zhou, M. Y. Ye, Y. F. Xiao, and G. C. Guo, “One-step implementation of a multiqubit controlled-phase-flip gate,” Phys. Rev. A 73, 012323 (2006). [CrossRef]
  44. G. S. Jin, Y. Lin, and B. Wu, “Generating multiphoton Greenberger-Horne-Zeilinger states with weak cross-Kerr nonlinearity,” Phys. Rev. A 75, 054302 (2007). [CrossRef]
  45. M. Paternostro, M. S. Kim, and B. S. Ham, “Generation of entangled coherent states via cross-phase-modulation in a double electromagnetically induced transparency regime,” Phys. Rev. A 67, 023811 (2003). [CrossRef]
  46. M. Bajcsy, A. S. Zibrov, and M. D. Lukin, “Stationary pulses of light in an atomic medium,” Nature 426, 638–641 (2003). [CrossRef] [PubMed]
  47. C. Wu, J. L. Chen, L. C. Kwek, and C. H. Oh, “Quantum nonlocality of N-qubit W states,” Phys. Rev. A 73, 012310 (2006). [CrossRef]
  48. K. Banaszek and K. Wódkiewicz, “Testing quantum nonlocality in phase space,” Phys. Rev. Lett. 82, 2009–2013 (1999). [CrossRef]
  49. B. S. Shi and T. Tomita, “Schemes for generating W state of paths and W state of polarization photons,” http://arxiv.org/abs/quant-ph/0208170.
  50. X. B. Zou, K. Pahlke, and W. Mathis, “Generation of an entangled four-photon W state,” Phys. Rev. A 66, 044302 (2002). [CrossRef]
  51. J. W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement,” Nature 403, 515–519 (2000). [CrossRef] [PubMed]
  52. H. F. Wang and S. Zhang, “Linear optical generation of multipartite entanglement with conventional photon detectors,” Phys. Rev. A 79, 042336 (2009). [CrossRef]
  53. D. Bouwmeester, J. W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349 (1999). [CrossRef]
  54. H. F. Wang and S. Zhang, “Scheme for linear optical preparation of a type of four-photon entangled state with conventional photon detectors,” Eur. Phys. J. D 53, 359–363 (2009). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


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

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited