Abstract

We present two schemes to concentrate unknown partially entangled three-photon W states with weak cross-Kerr nonlinearity. In both schemes, the three distant parities can obtain a maximally entangled W state via local operations and classical communication with a higher success probability that is double that in Xiong and Ye’s scheme [J. Opt. Soc. Am. B 28, 2030 (2011) [CrossRef]  ]. The entanglement concentration schemes need only one party’s local operations. Our schemes are relatively simple because fewer linear optics elements are used. In addition, our schemes do not need to use sophisticated single-photon detectors, which makes the scheme more feasible with present techniques.

© 2012 Optical Society of America

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  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]
  2. J. Joo, Y. J. Park, S. Oh, and J. Kim, “Quantum teleportation via a W state,” New J. Phys. 5, 136 (2003).
    [CrossRef]
  3. Z. L. Cao and M. Yang, “Probabilistic teleportation of unknown atomic state using W class states,” Physica A 337, 132–140 (2004).
    [CrossRef]
  4. P. Agrawal and A. Pati, “Perfect teleportation and superdense coding with W states,” Phys. Rev. A 74, 062320 (2006).
    [CrossRef]
  5. S. Muralidharan and P. K. Panigrahi, “Quantum-information splitting using multipartite cluster states,” Phys. Rev. A 78, 062333 (2008).
    [CrossRef]
  6. M. Murao and V. Vedral, “Remote information concentration using a bound entangled state,” Phys. Rev. Lett. 86, 352–355 (2001).
    [CrossRef]
  7. 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]
  8. 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]
  9. T. Yamamoto, M. Koashi, and N. Imoto, “Concentration and purification scheme for two partially entangled photon pairs,” Phys. Rev. A 64, 012304 (2001).
    [CrossRef]
  10. Z. Zhao, J. W. Pan, and M. S. Zhan, “Practical scheme for entanglement concentration,” Phys. Rev. A 64, 014301 (2001).
    [CrossRef]
  11. 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]
  12. 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]
  13. M. Yang, W. Song, and Z. L. Cao, “Entanglement purification for arbitrary unknown ionic states via linear optics,” Phys. Rev. A 71, 012308 (2005).
  14. M. Yang and Z. L. Cao, “Entanglement distillation for W class states,” Physica A 337, 141–148 (2004).
    [CrossRef]
  15. C. D. Ogden, M. Paternostro, and M. S. Kim, “Concentration and purification of entanglement for qubit systems with ancillary cavity fields,” Phys. Rev. A 75, 042325 (2007).
    [CrossRef]
  16. B. Fortescue and H. K. Lo, “Random bipartite entanglement from W and W-like states,” Phys. Rev. Lett. 98, 260501 (2007).
    [CrossRef]
  17. Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Efficient polarization entanglement concentration for electrons with charge detection,” Phys. Lett. A 373, 1823–1825 (2009).
    [CrossRef]
  18. 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]
  19. 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]
  20. 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]
  21. A. Miyake and H. J. Briegel, “Distillation of multipartite entanglement by complementary stabilizer measurements,” Phys. Rev. Lett. 95, 220501 (2005).
    [CrossRef]
  22. W. Dür and H. J. Briegel, “Entanglement purification and quantum error correction,” Rep. Prog. Phys. 70, 1381–1424 (2007).
    [CrossRef]
  23. M. Czechlewski, A. Grudka, S. Ishizaka, and A. Wójcik, “Entanglement purification protocol for a mixture of a pure entangled state and a pure product state,” Phys. Rev. A 80, 014303 (2009).
    [CrossRef]
  24. E. Isasi and D. Mundarain, “Distillation of Bell states in open systems,” Phys. Rev. A 81, 044303 (2010).
    [CrossRef]
  25. X. H. Li, “Deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044304 (2010).
    [CrossRef]
  26. Y. B. Sheng and F. G. Deng, “One-step deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044305 (2010).
    [CrossRef]
  27. Y. B. Sheng, F. G. Deng, and G. L. Long, “Multipartite electronic entanglement purification with charge detection,” Phys. Lett. A 375, 396–400 (2011).
    [CrossRef]
  28. Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity,” Phys. Rev. A 77, 042308 (2008).
    [CrossRef]
  29. Y. B. Sheng, F. G. Deng, B. K. Zhao, T. J. Wang, and H. Y. Zhou, “Multipartite entanglement purification with quantum nondemolition detectors,” Eur. Phys. J. D 55, 235–242 (2009).
    [CrossRef]
  30. Y. B. Sheng and F. G. Deng, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A 81, 032307 (2010).
    [CrossRef]
  31. F. G. Deng, “Efficient multipartite entanglement purification with the entanglement link from a subspace,” Phys. Rev. A 84, 052312 (2011).
    [CrossRef]
  32. 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).
  33. Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Single-photon entanglement concentration for long-distance quantum communication,” Quantum Inf. Comput. 10, 272–281 (2010).
  34. C. Wang, Y. Zhang, and G. S. Jin, “Polarization-entanglement purification and concentration using cross-Kerr nonlinearity,” Quantum Inf. Comput. 11, 988–1002 (2011).
  35. 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]
  36. P. Kok, H. Lee, and J. P. Dowling, “Single-photon quantum-nondemolition detectors constructed with linear optics and projective measurements,” Phys. Rev. A 66, 063814 (2002).
    [CrossRef]
  37. K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
    [CrossRef]
  38. M. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
    [CrossRef]
  39. J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Phys. 9, 16 (2007).
    [CrossRef]
  40. Q. Lin and J. Li, “Quantum control gates with weak cross-Kerr nonlinearity,” Phys. Rev. A 79, 022301 (2009).
  41. Q. Guo, J. Bai, L. Y. Cheng, X. Q. Shao, H. F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).
  42. W. Xiong and L. Ye, “Schemes for entanglement concentration of two unknown partially entangled states with cross-Kerr nonlinearity,” J. Opt. Soc. Am. B 28, 2030–2037 (2011).
    [CrossRef]
  43. C. Zhao, M. Zhu, and L. Ye, “Robust scheme for the preparation of polarization-photon cluster state with homodyne measurement via weak cross-Kerr nonlinearity,” J. Opt. Soc. Am. B 28, 1740–1745 (2011).
    [CrossRef]
  44. W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
    [CrossRef]
  45. P. Kok, “Effects of self-phase-modulation on weak nonlinear optical quantum gates,” Phys. Rev. A 77, 013808 (2008).
    [CrossRef]

2011

Y. B. Sheng, F. G. Deng, and G. L. Long, “Multipartite electronic entanglement purification with charge detection,” Phys. Lett. A 375, 396–400 (2011).
[CrossRef]

F. G. Deng, “Efficient multipartite entanglement purification with the entanglement link from a subspace,” Phys. Rev. A 84, 052312 (2011).
[CrossRef]

C. Wang, Y. Zhang, and G. S. Jin, “Polarization-entanglement purification and concentration using cross-Kerr nonlinearity,” Quantum Inf. Comput. 11, 988–1002 (2011).

Q. Guo, J. Bai, L. Y. Cheng, X. Q. Shao, H. F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).

C. Zhao, M. Zhu, and L. Ye, “Robust scheme for the preparation of polarization-photon cluster state with homodyne measurement via weak cross-Kerr nonlinearity,” J. Opt. Soc. Am. B 28, 1740–1745 (2011).
[CrossRef]

W. Xiong and L. Ye, “Schemes for entanglement concentration of two unknown partially entangled states with cross-Kerr nonlinearity,” J. Opt. Soc. Am. B 28, 2030–2037 (2011).
[CrossRef]

2010

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]

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

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

E. Isasi and D. Mundarain, “Distillation of Bell states in open systems,” Phys. Rev. A 81, 044303 (2010).
[CrossRef]

X. H. Li, “Deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044304 (2010).
[CrossRef]

Y. B. Sheng and F. G. Deng, “One-step deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044305 (2010).
[CrossRef]

2009

M. Czechlewski, A. Grudka, S. Ishizaka, and A. Wójcik, “Entanglement purification protocol for a mixture of a pure entangled state and a pure product state,” Phys. Rev. A 80, 014303 (2009).
[CrossRef]

Y. B. Sheng, F. G. Deng, B. K. Zhao, T. J. Wang, and H. Y. Zhou, “Multipartite entanglement purification with quantum nondemolition detectors,” Eur. Phys. J. D 55, 235–242 (2009).
[CrossRef]

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Efficient polarization entanglement concentration for electrons with charge detection,” Phys. Lett. A 373, 1823–1825 (2009).
[CrossRef]

Q. Lin and J. Li, “Quantum control gates with weak cross-Kerr nonlinearity,” Phys. Rev. A 79, 022301 (2009).

2008

P. Kok, “Effects of self-phase-modulation on weak nonlinear optical quantum gates,” Phys. Rev. A 77, 013808 (2008).
[CrossRef]

S. Muralidharan and P. K. Panigrahi, “Quantum-information splitting using multipartite cluster states,” Phys. Rev. A 78, 062333 (2008).
[CrossRef]

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).

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

2007

W. Dür and H. J. Briegel, “Entanglement purification and quantum error correction,” Rep. Prog. Phys. 70, 1381–1424 (2007).
[CrossRef]

C. D. Ogden, M. Paternostro, and M. S. Kim, “Concentration and purification of entanglement for qubit systems with ancillary cavity fields,” Phys. Rev. A 75, 042325 (2007).
[CrossRef]

B. Fortescue and H. K. Lo, “Random bipartite entanglement from W and W-like states,” Phys. Rev. Lett. 98, 260501 (2007).
[CrossRef]

J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Phys. 9, 16 (2007).
[CrossRef]

2006

P. Agrawal and A. Pati, “Perfect teleportation and superdense coding with W states,” Phys. Rev. A 74, 062320 (2006).
[CrossRef]

2005

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]

M. Yang, W. Song, and Z. L. Cao, “Entanglement purification for arbitrary unknown ionic states via linear optics,” Phys. Rev. A 71, 012308 (2005).

A. Miyake and H. J. Briegel, “Distillation of multipartite entanglement by complementary stabilizer measurements,” Phys. Rev. Lett. 95, 220501 (2005).
[CrossRef]

M. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
[CrossRef]

W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[CrossRef]

2004

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
[CrossRef]

M. Yang and Z. L. Cao, “Entanglement distillation for W class states,” Physica A 337, 141–148 (2004).
[CrossRef]

Z. L. Cao and M. Yang, “Probabilistic teleportation of unknown atomic state using W class states,” Physica A 337, 132–140 (2004).
[CrossRef]

2003

J. Joo, Y. J. Park, S. Oh, and J. Kim, “Quantum teleportation via a W state,” New J. Phys. 5, 136 (2003).
[CrossRef]

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]

2002

P. Kok, H. Lee, and J. P. Dowling, “Single-photon quantum-nondemolition detectors constructed with linear optics and projective measurements,” Phys. Rev. A 66, 063814 (2002).
[CrossRef]

2001

M. Murao and V. Vedral, “Remote information concentration using a bound entangled state,” Phys. Rev. Lett. 86, 352–355 (2001).
[CrossRef]

T. Yamamoto, M. Koashi, and N. Imoto, “Concentration and purification scheme for two partially entangled photon pairs,” Phys. Rev. A 64, 012304 (2001).
[CrossRef]

Z. Zhao, J. W. Pan, and M. S. Zhan, “Practical scheme for entanglement concentration,” Phys. Rev. A 64, 014301 (2001).
[CrossRef]

1996

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]

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]

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]

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]

1993

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]

1985

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]

Agrawal, P.

P. Agrawal and A. Pati, “Perfect teleportation and superdense coding with W states,” Phys. Rev. A 74, 062320 (2006).
[CrossRef]

Bai, J.

Q. Guo, J. Bai, L. Y. Cheng, X. Q. Shao, H. F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).

Beausoleil, R. G.

W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[CrossRef]

Bennett, C. H.

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]

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]

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]

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]

Bernstein, H. J.

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]

Brassard, G.

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]

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]

Briegel, H. J.

W. Dür and H. J. Briegel, “Entanglement purification and quantum error correction,” Rep. Prog. Phys. 70, 1381–1424 (2007).
[CrossRef]

A. Miyake and H. J. Briegel, “Distillation of multipartite entanglement by complementary stabilizer measurements,” Phys. Rev. Lett. 95, 220501 (2005).
[CrossRef]

Cao, Z. L.

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]

M. Yang, W. Song, and Z. L. Cao, “Entanglement purification for arbitrary unknown ionic states via linear optics,” Phys. Rev. A 71, 012308 (2005).

M. Yang and Z. L. Cao, “Entanglement distillation for W class states,” Physica A 337, 141–148 (2004).
[CrossRef]

Z. L. Cao and M. Yang, “Probabilistic teleportation of unknown atomic state using W class states,” Physica A 337, 132–140 (2004).
[CrossRef]

Chen, Y. A.

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]

Cheng, L. Y.

Q. Guo, J. Bai, L. Y. Cheng, X. Q. Shao, H. F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).

Crépeau, C.

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]

Czechlewski, M.

M. Czechlewski, A. Grudka, S. Ishizaka, and A. Wójcik, “Entanglement purification protocol for a mixture of a pure entangled state and a pure product state,” Phys. Rev. A 80, 014303 (2009).
[CrossRef]

Deng, F. G.

Y. B. Sheng, F. G. Deng, and G. L. Long, “Multipartite electronic entanglement purification with charge detection,” Phys. Lett. A 375, 396–400 (2011).
[CrossRef]

F. G. Deng, “Efficient multipartite entanglement purification with the entanglement link from a subspace,” Phys. Rev. A 84, 052312 (2011).
[CrossRef]

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

Y. B. Sheng and F. G. Deng, “One-step deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044305 (2010).
[CrossRef]

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

Y. B. Sheng, F. G. Deng, B. K. Zhao, T. J. Wang, and H. Y. Zhou, “Multipartite entanglement purification with quantum nondemolition detectors,” Eur. Phys. J. D 55, 235–242 (2009).
[CrossRef]

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Efficient polarization entanglement concentration for electrons with charge detection,” Phys. Lett. A 373, 1823–1825 (2009).
[CrossRef]

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).

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

Deutsch, D.

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]

DiVincenzo, D. P.

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]

Dowling, J. P.

P. Kok, H. Lee, and J. P. Dowling, “Single-photon quantum-nondemolition detectors constructed with linear optics and projective measurements,” Phys. Rev. A 66, 063814 (2002).
[CrossRef]

Dür, W.

W. Dür and H. J. Briegel, “Entanglement purification and quantum error correction,” Rep. Prog. Phys. 70, 1381–1424 (2007).
[CrossRef]

Ekert, A.

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]

Fortescue, B.

B. Fortescue and H. K. Lo, “Random bipartite entanglement from W and W-like states,” Phys. Rev. Lett. 98, 260501 (2007).
[CrossRef]

Grudka, A.

M. Czechlewski, A. Grudka, S. Ishizaka, and A. Wójcik, “Entanglement purification protocol for a mixture of a pure entangled state and a pure product state,” Phys. Rev. A 80, 014303 (2009).
[CrossRef]

Guo, Q.

Q. Guo, J. Bai, L. Y. Cheng, X. Q. Shao, H. F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).

Haus, H. A.

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]

Imoto, N.

T. Yamamoto, M. Koashi, and N. Imoto, “Concentration and purification scheme for two partially entangled photon pairs,” Phys. Rev. A 64, 012304 (2001).
[CrossRef]

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]

Isasi, E.

E. Isasi and D. Mundarain, “Distillation of Bell states in open systems,” Phys. Rev. A 81, 044303 (2010).
[CrossRef]

Ishizaka, S.

M. Czechlewski, A. Grudka, S. Ishizaka, and A. Wójcik, “Entanglement purification protocol for a mixture of a pure entangled state and a pure product state,” Phys. Rev. A 80, 014303 (2009).
[CrossRef]

Jin, G. S.

C. Wang, Y. Zhang, and G. S. Jin, “Polarization-entanglement purification and concentration using cross-Kerr nonlinearity,” Quantum Inf. Comput. 11, 988–1002 (2011).

Joo, J.

J. Joo, Y. J. Park, S. Oh, and J. Kim, “Quantum teleportation via a W state,” New J. Phys. 5, 136 (2003).
[CrossRef]

Jozsa, R.

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]

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]

Kim, J.

J. Joo, Y. J. Park, S. Oh, and J. Kim, “Quantum teleportation via a W state,” New J. Phys. 5, 136 (2003).
[CrossRef]

Kim, M. S.

C. D. Ogden, M. Paternostro, and M. S. Kim, “Concentration and purification of entanglement for qubit systems with ancillary cavity fields,” Phys. Rev. A 75, 042325 (2007).
[CrossRef]

Koashi, M.

T. Yamamoto, M. Koashi, and N. Imoto, “Concentration and purification scheme for two partially entangled photon pairs,” Phys. Rev. A 64, 012304 (2001).
[CrossRef]

Kok, P.

P. Kok, “Effects of self-phase-modulation on weak nonlinear optical quantum gates,” Phys. Rev. A 77, 013808 (2008).
[CrossRef]

P. Kok, H. Lee, and J. P. Dowling, “Single-photon quantum-nondemolition detectors constructed with linear optics and projective measurements,” Phys. Rev. A 66, 063814 (2002).
[CrossRef]

Lee, H.

P. Kok, H. Lee, and J. P. Dowling, “Single-photon quantum-nondemolition detectors constructed with linear optics and projective measurements,” Phys. Rev. A 66, 063814 (2002).
[CrossRef]

Li, J.

Q. Lin and J. Li, “Quantum control gates with weak cross-Kerr nonlinearity,” Phys. Rev. A 79, 022301 (2009).

Li, X. H.

X. H. Li, “Deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044304 (2010).
[CrossRef]

Lin, Q.

Q. Lin and J. Li, “Quantum control gates with weak cross-Kerr nonlinearity,” Phys. Rev. A 79, 022301 (2009).

Lo, H. K.

B. Fortescue and H. K. Lo, “Random bipartite entanglement from W and W-like states,” Phys. Rev. Lett. 98, 260501 (2007).
[CrossRef]

Long, G. L.

Y. B. Sheng, F. G. Deng, and G. L. Long, “Multipartite electronic entanglement purification with charge detection,” Phys. Lett. A 375, 396–400 (2011).
[CrossRef]

Macchiavello, C.

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]

Miyake, A.

A. Miyake and H. J. Briegel, “Distillation of multipartite entanglement by complementary stabilizer measurements,” Phys. Rev. Lett. 95, 220501 (2005).
[CrossRef]

Mundarain, D.

E. Isasi and D. Mundarain, “Distillation of Bell states in open systems,” Phys. Rev. A 81, 044303 (2010).
[CrossRef]

Munro, M. J.

M. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
[CrossRef]

Munro, W. J.

W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[CrossRef]

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
[CrossRef]

Muralidharan, S.

S. Muralidharan and P. K. Panigrahi, “Quantum-information splitting using multipartite cluster states,” Phys. Rev. A 78, 062333 (2008).
[CrossRef]

Murao, M.

M. Murao and V. Vedral, “Remote information concentration using a bound entangled state,” Phys. Rev. Lett. 86, 352–355 (2001).
[CrossRef]

Nemoto, K.

W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[CrossRef]

M. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
[CrossRef]

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
[CrossRef]

Ogden, C. D.

C. D. Ogden, M. Paternostro, and M. S. Kim, “Concentration and purification of entanglement for qubit systems with ancillary cavity fields,” Phys. Rev. A 75, 042325 (2007).
[CrossRef]

Oh, S.

J. Joo, Y. J. Park, S. Oh, and J. Kim, “Quantum teleportation via a W state,” New J. Phys. 5, 136 (2003).
[CrossRef]

Pan, J. W.

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]

Z. Zhao, J. W. Pan, and M. S. Zhan, “Practical scheme for entanglement concentration,” Phys. Rev. A 64, 014301 (2001).
[CrossRef]

Panigrahi, P. K.

S. Muralidharan and P. K. Panigrahi, “Quantum-information splitting using multipartite cluster states,” Phys. Rev. A 78, 062333 (2008).
[CrossRef]

Park, Y. J.

J. Joo, Y. J. Park, S. Oh, and J. Kim, “Quantum teleportation via a W state,” New J. Phys. 5, 136 (2003).
[CrossRef]

Paternostro, M.

C. D. Ogden, M. Paternostro, and M. S. Kim, “Concentration and purification of entanglement for qubit systems with ancillary cavity fields,” Phys. Rev. A 75, 042325 (2007).
[CrossRef]

Pati, A.

P. Agrawal and A. Pati, “Perfect teleportation and superdense coding with W states,” Phys. Rev. A 74, 062320 (2006).
[CrossRef]

Peres, A.

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]

Popescu, S.

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]

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]

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]

Razavi, M.

J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Phys. 9, 16 (2007).
[CrossRef]

Sanpera, A.

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]

Schumacher, B.

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]

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]

Shao, X. Q.

Q. Guo, J. Bai, L. Y. Cheng, X. Q. Shao, H. F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).

Shapiro, J. H.

J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Phys. 9, 16 (2007).
[CrossRef]

Sheng, Y. B.

Y. B. Sheng, F. G. Deng, and G. L. Long, “Multipartite electronic entanglement purification with charge detection,” Phys. Lett. A 375, 396–400 (2011).
[CrossRef]

Y. B. Sheng and F. G. Deng, “One-step deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044305 (2010).
[CrossRef]

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

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

Y. B. Sheng, F. G. Deng, B. K. Zhao, T. J. Wang, and H. Y. Zhou, “Multipartite entanglement purification with quantum nondemolition detectors,” Eur. Phys. J. D 55, 235–242 (2009).
[CrossRef]

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Efficient polarization entanglement concentration for electrons with charge detection,” Phys. Lett. A 373, 1823–1825 (2009).
[CrossRef]

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).

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

Smolin, J. A.

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]

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]

Song, W.

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]

M. Yang, W. Song, and Z. L. Cao, “Entanglement purification for arbitrary unknown ionic states via linear optics,” Phys. Rev. A 71, 012308 (2005).

Spiller, T. P.

M. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
[CrossRef]

W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[CrossRef]

Vedral, V.

M. Murao and V. Vedral, “Remote information concentration using a bound entangled state,” Phys. Rev. Lett. 86, 352–355 (2001).
[CrossRef]

Wang, C.

C. Wang, Y. Zhang, and G. S. Jin, “Polarization-entanglement purification and concentration using cross-Kerr nonlinearity,” Quantum Inf. Comput. 11, 988–1002 (2011).

Wang, H. F.

Q. Guo, J. Bai, L. Y. Cheng, X. Q. Shao, H. F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).

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]

Wang, T. J.

Y. B. Sheng, F. G. Deng, B. K. Zhao, T. J. Wang, and H. Y. Zhou, “Multipartite entanglement purification with quantum nondemolition detectors,” Eur. Phys. J. D 55, 235–242 (2009).
[CrossRef]

Wójcik, A.

M. Czechlewski, A. Grudka, S. Ishizaka, and A. Wójcik, “Entanglement purification protocol for a mixture of a pure entangled state and a pure product state,” Phys. Rev. A 80, 014303 (2009).
[CrossRef]

Wootters, W. K.

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]

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]

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]

Xiong, W.

Yamamoto, T.

T. Yamamoto, M. Koashi, and N. Imoto, “Concentration and purification scheme for two partially entangled photon pairs,” Phys. Rev. A 64, 012304 (2001).
[CrossRef]

Yamamoto, Y.

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]

Yang, M.

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]

M. Yang, W. Song, and Z. L. Cao, “Entanglement purification for arbitrary unknown ionic states via linear optics,” Phys. Rev. A 71, 012308 (2005).

Z. L. Cao and M. Yang, “Probabilistic teleportation of unknown atomic state using W class states,” Physica A 337, 132–140 (2004).
[CrossRef]

M. Yang and Z. L. Cao, “Entanglement distillation for W class states,” Physica A 337, 141–148 (2004).
[CrossRef]

Yang, T.

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]

Ye, L.

Yeon, K. H.

Zhan, M. S.

Z. Zhao, J. W. Pan, and M. S. Zhan, “Practical scheme for entanglement concentration,” Phys. Rev. A 64, 014301 (2001).
[CrossRef]

Zhang, A. N.

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]

Zhang, S.

Q. Guo, J. Bai, L. Y. Cheng, X. Q. Shao, H. F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).

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]

Zhang, Y.

C. Wang, Y. Zhang, and G. S. Jin, “Polarization-entanglement purification and concentration using cross-Kerr nonlinearity,” Quantum Inf. Comput. 11, 988–1002 (2011).

Zhao, B. K.

Y. B. Sheng, F. G. Deng, B. K. Zhao, T. J. Wang, and H. Y. Zhou, “Multipartite entanglement purification with quantum nondemolition detectors,” Eur. Phys. J. D 55, 235–242 (2009).
[CrossRef]

Zhao, C.

Zhao, Y.

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]

Zhao, Z.

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]

Z. Zhao, J. W. Pan, and M. S. Zhan, “Practical scheme for entanglement concentration,” Phys. Rev. A 64, 014301 (2001).
[CrossRef]

Zhou, H. Y.

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

Y. B. Sheng, F. G. Deng, B. K. Zhao, T. J. Wang, and H. Y. Zhou, “Multipartite entanglement purification with quantum nondemolition detectors,” Eur. Phys. J. D 55, 235–242 (2009).
[CrossRef]

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Efficient polarization entanglement concentration for electrons with charge detection,” Phys. Lett. A 373, 1823–1825 (2009).
[CrossRef]

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).

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

Zhu, M.

Eur. Phys. J. D

Y. B. Sheng, F. G. Deng, B. K. Zhao, T. J. Wang, and H. Y. Zhou, “Multipartite entanglement purification with quantum nondemolition detectors,” Eur. Phys. J. D 55, 235–242 (2009).
[CrossRef]

J. Opt. Soc. Am. B

New J. Phys.

M. J. Munro, K. Nemoto, and T. P. Spiller, “Weak nonlinearities: a new route to optical quantum computation,” New J. Phys. 7, 137 (2005).
[CrossRef]

J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Phys. 9, 16 (2007).
[CrossRef]

J. Joo, Y. J. Park, S. Oh, and J. Kim, “Quantum teleportation via a W state,” New J. Phys. 5, 136 (2003).
[CrossRef]

Phys. Lett. A

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Efficient polarization entanglement concentration for electrons with charge detection,” Phys. Lett. A 373, 1823–1825 (2009).
[CrossRef]

Y. B. Sheng, F. G. Deng, and G. L. Long, “Multipartite electronic entanglement purification with charge detection,” Phys. Lett. A 375, 396–400 (2011).
[CrossRef]

Phys. Rev. A

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

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]

P. Kok, H. Lee, and J. P. Dowling, “Single-photon quantum-nondemolition detectors constructed with linear optics and projective measurements,” Phys. Rev. A 66, 063814 (2002).
[CrossRef]

Q. Lin and J. Li, “Quantum control gates with weak cross-Kerr nonlinearity,” Phys. Rev. A 79, 022301 (2009).

Q. Guo, J. Bai, L. Y. Cheng, X. Q. Shao, H. F. Wang, and S. Zhang, “Simplified optical quantum-information processing via weak cross-Kerr nonlinearities,” Phys. Rev. A 83, 054303 (2011).

W. J. Munro, K. Nemoto, R. G. Beausoleil, and T. P. Spiller, “High-efficiency quantum nondemolition single-photon-number-resolving detector,” Phys. Rev. A 71, 033819 (2005).
[CrossRef]

P. Kok, “Effects of self-phase-modulation on weak nonlinear optical quantum gates,” Phys. Rev. A 77, 013808 (2008).
[CrossRef]

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

F. G. Deng, “Efficient multipartite entanglement purification with the entanglement link from a subspace,” Phys. Rev. A 84, 052312 (2011).
[CrossRef]

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).

M. Czechlewski, A. Grudka, S. Ishizaka, and A. Wójcik, “Entanglement purification protocol for a mixture of a pure entangled state and a pure product state,” Phys. Rev. A 80, 014303 (2009).
[CrossRef]

E. Isasi and D. Mundarain, “Distillation of Bell states in open systems,” Phys. Rev. A 81, 044303 (2010).
[CrossRef]

X. H. Li, “Deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044304 (2010).
[CrossRef]

Y. B. Sheng and F. G. Deng, “One-step deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044305 (2010).
[CrossRef]

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]

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]

M. Yang, W. Song, and Z. L. Cao, “Entanglement purification for arbitrary unknown ionic states via linear optics,” Phys. Rev. A 71, 012308 (2005).

C. D. Ogden, M. Paternostro, and M. S. Kim, “Concentration and purification of entanglement for qubit systems with ancillary cavity fields,” Phys. Rev. A 75, 042325 (2007).
[CrossRef]

P. Agrawal and A. Pati, “Perfect teleportation and superdense coding with W states,” Phys. Rev. A 74, 062320 (2006).
[CrossRef]

S. Muralidharan and P. K. Panigrahi, “Quantum-information splitting using multipartite cluster states,” Phys. Rev. A 78, 062333 (2008).
[CrossRef]

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]

T. Yamamoto, M. Koashi, and N. Imoto, “Concentration and purification scheme for two partially entangled photon pairs,” Phys. Rev. A 64, 012304 (2001).
[CrossRef]

Z. Zhao, J. W. Pan, and M. S. Zhan, “Practical scheme for entanglement concentration,” Phys. Rev. A 64, 014301 (2001).
[CrossRef]

Phys. Rev. Lett.

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]

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]

M. Murao and V. Vedral, “Remote information concentration using a bound entangled state,” Phys. Rev. Lett. 86, 352–355 (2001).
[CrossRef]

B. Fortescue and H. K. Lo, “Random bipartite entanglement from W and W-like states,” Phys. Rev. Lett. 98, 260501 (2007).
[CrossRef]

A. Miyake and H. J. Briegel, “Distillation of multipartite entanglement by complementary stabilizer measurements,” Phys. Rev. Lett. 95, 220501 (2005).
[CrossRef]

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]

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
[CrossRef]

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]

Physica A

M. Yang and Z. L. Cao, “Entanglement distillation for W class states,” Physica A 337, 141–148 (2004).
[CrossRef]

Z. L. Cao and M. Yang, “Probabilistic teleportation of unknown atomic state using W class states,” Physica A 337, 132–140 (2004).
[CrossRef]

Quantum Inf. Comput.

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

C. Wang, Y. Zhang, and G. S. Jin, “Polarization-entanglement purification and concentration using cross-Kerr nonlinearity,” Quantum Inf. Comput. 11, 988–1002 (2011).

Rep. Prog. Phys.

W. Dür and H. J. Briegel, “Entanglement purification and quantum error correction,” Rep. Prog. Phys. 70, 1381–1424 (2007).
[CrossRef]

Cited By

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Figures (4)

Fig. 1.
Fig. 1.

Schematic diagram of concentrating two unknown and partially entangled three-photon W states.

Fig. 2.
Fig. 2.

(a) Two qubit polarization parity QND detector with a classical feedforward. ϕ(X) is a phase shift dependent on the result of the homodyne measurement. (b) Schematic version of (a).

Fig. 3.
Fig. 3.

Schematic diagram of entanglement concentration with two polarization parity QND detectors.

Fig. 4.
Fig. 4.

Schematic diagram of obtaining reusable entanglement.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

|Φ123=a|H1|H2|V3+b(|H1|V2|H3+|V1|H2|H3),
|Ψ0=|Φ123|Φ456|αp,
|Ψ1=|φ0|αp+|φ1|αeiθp+|φ1|αeiθp+|φ2|αei2θp,
|φ0=ab(|H1|H2|Va2|H4|Va4|Ha5+|H1|V2|Ha1|H4|Ha3|Va6+|V1|H2|Ha1|H4|Ha3|Va6),|φ1=a2|H1|H2|Va2|H4|Ha3|Va6+b2(|H1|V2|Ha1|V4|Ha3|Ha5+|V1|H2|Ha1|V4|Ha3|Ha5),|φ1=b2(|H1|V2|Ha1|H4|Va4|Ha5+|V1|H2|Ha1|H4|Va4|Ha5),|φ2=ab|H1|H2|Va2|V4|Ha3|Ha5.
er|H12(|H+|V),|V12(|H|V),
|H12(|H+|V),|V12(|H+|V).
|Ψ3=ab2|H4[(|H1|H2|V3+|H1|V2|H3+|V1|H2|H3)(|H5|H6+|V5|V6)+(|H1|H2|V3+|H1|V2|H3+|V1|H2|H3)(|H5|V6+|V5|H6)].
|Ψ4=13(|H1|H2|V3+|H1|V2|H3+|V1|H2|H3),
|Ψ5=13(|H1|H2|V3+|H1|V2|H3+|V1|H2|H3),
|ΨII=12(|H1|V2+|V1|H2)(|H4|Va8+|V4|Ha8).
|Φ456|Φ4a1a9=b|H4(|Ha1|Va9+|Va1|Ha9).
|Φ2=ab(|H1|H2|V3|H4|Va8|Ha9+|H1|V2|H3|H4|Ha8|Va9+|V1|H2|H3|H4|Ha8|Va9).
|ΦI=a2|H1|H2|V3|H4|Ha8|Va9+b2|H1|V2|H3|H4|Va8|Ha9+b2|V1|H2|H3|H4|Va8|Ha9,
|ΦII=12{[a2|H1|H2|Va9+b2(|H1|V2|Ha9+|V1|H2|Ha9)](|H3|H5+|V3|V5)+[a2|H1|H2|Va9+b2(|H1|V2|Ha9+|V1|H2|Ha9)](|H3|V5+|V3|H5)}|H4.
|ΦIII=1|a|4+2|b|4[a2|H1|H2|Va9+b2(|H1|V2|Ha9+|V1|H2|Ha9)],

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