Abstract

We put forward an efficient entanglement concentration protocol (ECP) for recovering the single-photon less-entangled W state into the maximally entangled W state with only two conventional auxiliary photons. The ECP includes two local steps, both of which are based on the weak cross-Kerr nonlinearities and the variable beam splitter (VBS). Benefiting from the cross-Kerr nonlinearities and the VBS, the ECP can be used repeatedly to further concentrate the less-entangled W state. All the advantages indicate that our protocol may be feasible and convenient in current quantum communications areas.

© 2012 Optical Society of America

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  27. L. Heaney, A. Cabello, M. F. Santos, and V. Vedral, “Extreme nonlocality with one photon,” New J. Phys. 13, 053054–053065(2011).
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    [CrossRef]
  29. 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]
  30. S. Bose, V. Vedral, and P. L. Knight, “Purification via entanglement swapping and conserved entanglement,” Phys. Rev. A 60, 194–197 (1999).
    [CrossRef]
  31. B. S. Shi, Y. K. Jiang, and G. C. Guo, “Optimal entanglement purification via entanglement swapping,” Phys. Rev. A 62, 054301 (2000).
    [CrossRef]
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    [CrossRef]
  33. T. Yamamoto, M. Koashi, and N. Imoto, “Concentration and purification scheme for two partially entangled photon pairs,” Phys. Rev. A 64, 012304 (2001).
    [CrossRef]
  34. 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).
  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. Y. B. Sheng, L. Zhou, S. M. Zhao, and B. Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A 85, 012307 (2012).
    [CrossRef]
  37. F. G. Deng, “Optimal nonlocal multipartite entanglement concentration based on projection measurements,” Phys. Rev. A 85, 022311 (2012).
    [CrossRef]
  38. C. Wang, Y. Zhang, and G. S. Jin, “Entanglement purification and concentration of electron-spin entangled states using quantum-dot spins in optical microcavities,” Phys. Rev. A 84, 032307 (2011).
    [CrossRef]
  39. C. Wang, “Efficient entanglement concentration for partially entangled electrons using a quantum-dot and microcavity coupled system,” Phys. Rev. A 86, 012323 (2012).
    [CrossRef]
  40. H. F. Wang, L. L. Sun, S. Zhang, and K. H. Yeon, “Scheme for entanglement concentration of unknown partially entangled three-atom W states in cavity QED,” Quantum Inf. Process. 11, 431–441 (2012).
    [CrossRef]
  41. 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).
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  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. A. Yildiz, “Optimal distillation of three-qubit W states,” Phys. Rev. A 82, 012317 (2010).
    [CrossRef]
  44. H. F. Wang, S. Zhang, and K. H. Yeon, “Linear optical scheme for entanglement concentration of two partially entangled threephoton W states,” Eur. Phys. J. D 56, 271–275 (2010).
    [CrossRef]
  45. Y. B. Sheng, L. Zhou, and S. M. Zhao, “Efficient two-step entanglement concentration for arbitrary W states,” Phys. Rev. A 85, 044302 (2012).
    [CrossRef]
  46. F. F. Du, T. Li, B. C. Ren, H. R. Wei, and F. G. Deng, “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).
    [CrossRef]
  47. B. Gu, “Single-photon-assisted entanglement concentration of partially entangled multiphoton W states with linear optics,” J. Opt. Soc. Am. B 29, 1685–1689 (2012).
    [CrossRef]
  48. K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-nOT gate,” Phys. Rev. Lett. 93, 250502(2004).
    [CrossRef]
  49. Q. Lin and J. Li, “Quantum control gates with weak cross-Kerr nonlinearity,” Phys. Rev. A 79, 022301 (2009).
    [CrossRef]
  50. 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]
  51. 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]
  52. 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]
  53. Q. Lin and B. He, “Single-photon logic gates using minimal resources,” Phys. Rev. A 80, 042310 (2009).
    [CrossRef]
  54. Q. Lin and B. He, “Efficient generation of universal two-dimensional cluster states with hybrid systems,” Phys. Rev. A 82, 022331 (2010).
    [CrossRef]
  55. B. He, Y. Ren, and J. A. Bergou, “Creation of high-quality long-distance entanglement with flexible resources,” Phys. Rev. A 79, 052323 (2009).
    [CrossRef]
  56. B. He and J. A. Bergou, “Entanglement transformation with no classical communication,” Phys. Rev. A 78, 062328 (2008).
    [CrossRef]
  57. B. He, Q. Lin, and C. Simon, “Cross-Kerr nonlinearity between continuous-mode coherent states and single photons,” Phys. Rev. A 83, 053826 (2011).
    [CrossRef]
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    [CrossRef]
  59. M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
    [CrossRef]
  60. B. He, J. A. Bergou, and Z. Wang, “Implementation of quantum operations on single-photon qudits,” Phys. Rev. A 76, 042326 (2007).
    [CrossRef]
  61. H. Schmidt and A. Imamoğlu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21, 1936–1938 (1996).
    [CrossRef]
  62. C. Wang, Y. Zhang, and G. S. Jin, “Polarization-entanglement purification and concentration using cross-Kerr nonlinearity,” Quantum Inf. Comput. 11, 988–1002 (2011).
  63. 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]

2012 (8)

Y. B. Sheng, L. Zhou, S. M. Zhao, and B. Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A 85, 012307 (2012).
[CrossRef]

F. G. Deng, “Optimal nonlocal multipartite entanglement concentration based on projection measurements,” Phys. Rev. A 85, 022311 (2012).
[CrossRef]

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

H. F. Wang, L. L. Sun, S. Zhang, and K. H. Yeon, “Scheme for entanglement concentration of unknown partially entangled three-atom W states in cavity QED,” Quantum Inf. Process. 11, 431–441 (2012).
[CrossRef]

Y. B. Sheng, L. Zhou, and S. M. Zhao, “Efficient two-step entanglement concentration for arbitrary W states,” Phys. Rev. A 85, 044302 (2012).
[CrossRef]

F. F. Du, T. Li, B. C. Ren, H. R. Wei, and F. G. Deng, “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).
[CrossRef]

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

C. I. Osorio, N. Bruno, N. Sangouard, H. Zbinden, N. Gisin, and R. T. Thew, “Heralded photon amplification for quantum communication,” Phys. Rev. A 86, 023815 (2012).
[CrossRef]

2011 (5)

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

B. He, Q. Lin, and C. Simon, “Cross-Kerr nonlinearity between continuous-mode coherent states and single photons,” Phys. Rev. A 83, 053826 (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]

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

L. Heaney, A. Cabello, M. F. Santos, and V. Vedral, “Extreme nonlocality with one photon,” New J. Phys. 13, 053054–053065(2011).
[CrossRef]

2010 (7)

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).

R. Chaves, and L. Davidovich, “Robustness of entanglement as a resource,” Phys. Rev. A 82, 052308 (2010).
[CrossRef]

A. Yildiz, “Optimal distillation of three-qubit W states,” Phys. Rev. A 82, 012317 (2010).
[CrossRef]

H. F. Wang, S. Zhang, and K. H. Yeon, “Linear optical scheme for entanglement concentration of two partially entangled threephoton W states,” Eur. Phys. J. D 56, 271–275 (2010).
[CrossRef]

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

Q. Lin and B. He, “Efficient generation of universal two-dimensional cluster states with hybrid systems,” Phys. Rev. A 82, 022331 (2010).
[CrossRef]

2009 (3)

B. He, Y. Ren, and J. A. Bergou, “Creation of high-quality long-distance entanglement with flexible resources,” Phys. Rev. A 79, 052323 (2009).
[CrossRef]

Q. Lin and B. He, “Single-photon logic gates using minimal resources,” Phys. Rev. A 80, 042310 (2009).
[CrossRef]

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

2008 (3)

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]

B. He and J. A. Bergou, “Entanglement transformation with no classical communication,” Phys. Rev. A 78, 062328 (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).
[CrossRef]

2007 (1)

B. He, J. A. Bergou, and Z. Wang, “Implementation of quantum operations on single-photon qudits,” Phys. Rev. A 76, 042326 (2007).
[CrossRef]

2005 (4)

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]

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]

F. G. Deng, C. Y. Li, Y. S. Li, H. Y. Zhou, and Y. Wang, “Symmetric multiparty-controlled teleportation of an arbitrary two-particle entanglement,” Phys. Rev. A 72, 022338 (2005).
[CrossRef]

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

2004 (1)

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-nOT gate,” Phys. Rev. Lett. 93, 250502(2004).
[CrossRef]

2003 (6)

M. G. A. Paris, M. Cola, and R. Bonifacio, “Quantum state engeneering assisted by entanglement,” Phys. Rev. A 67, 042104 (2003).
[CrossRef]

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

J. Jing, J. Zhang, Y. Yan, F. Zhao, C. Xie, and K. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90, 167903–167906 (2003).
[CrossRef]

T. Aoki, N. Takey, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, and P. van Loock, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404–080407 (2003).
[CrossRef]

O. Göckl, S. Lorenz, C. Marquardt, J. Heersink, M. Brownnutt, C. Silberhorn, Q. Pan, P. van Loock, N. Korolkova, and G. Leuchs, “Experiment towards continuous-variable entanglement swapping: highly correlated four-partite quantum state,” Phys. Rev. A 68, 012319 (2003).
[CrossRef]

A. SenDe, U. Sen, M. Wieśniak, D. Kaszlikowski, and M. Żukowski, “Multiqubit W states lead to stronger nonclassicality than Greenberger-Horne-Zeilinger states,” Phys. Rev. A 68, 062306 (2003).
[CrossRef]

2002 (4)

C. Silberhorn, T. C. Ralph, N. Lütkenhaus, and G. Leuchs, “Continuous variable quantum cryptography: beating the 3 dB loss limit,” Phys. Rev. Lett. 89, 167901–167904 (2002).
[CrossRef]

Ch. Silberhorn, N. Korolkova, and G. Leuchs, “Quantum key distribution with bright entangled beams,” Phys. Rev. Lett. 88, 167902–167905 (2002).
[CrossRef]

G. L. Long and X. S. Liu, “Theoretically efficient high-capacity quantum-key-distribution scheme,” Phys. Rev. A 65, 032302 (2002).
[CrossRef]

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[CrossRef]

2001 (5)

G. M. D’Ariano and P. Lo Presti, “Quantum tomography for measuring experimentally the matrix elements of an arbitrary quantum operation,” Phys. Rev. Lett. 86, 4195–4198 (2001).
[CrossRef]

G. M. D’Ariano, P. Lo Presti, and M. G. A. Paris, “Using entanglement improves the precision of quantum measurements,” Phys. Rev. Lett. 87, 270404–270407 (2001).
[CrossRef]

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

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

2000 (2)

W. Dür, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62, 062314 (2000).
[CrossRef]

B. S. Shi, Y. K. Jiang, and G. C. Guo, “Optimal entanglement purification via entanglement swapping,” Phys. Rev. A 62, 054301 (2000).
[CrossRef]

1999 (1)

S. Bose, V. Vedral, and P. L. Knight, “Purification via entanglement swapping and conserved entanglement,” Phys. Rev. A 60, 194–197 (1999).
[CrossRef]

1998 (2)

A. Furusawa, J. L. Søensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
[CrossRef]

A. Karlsson and M. Bourennane, “Quantum teleportation using three-particle entanglement,” Phys. Rev. A 58, 4394 (1998).
[CrossRef]

1996 (2)

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]

H. Schmidt and A. Imamoğlu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21, 1936–1938 (1996).
[CrossRef]

1995 (1)

A. Peres, “Nonlocal effects in Fock space,” Phys. Rev. Lett. 74, 4571–4571 (1995).
[CrossRef]

1994 (2)

L. Hardy, “Nonlocality of a single photon revisited,” Phys. Rev. Lett. 73, 2279–2283 (1994).
[CrossRef]

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
[CrossRef]

1993 (1)

C. H. Bennett, G. Brassard, C. Crepeau, 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]

1992 (1)

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]

1991 (2)

A. K. Ekert, “Quantum cryptography based on Bells theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[CrossRef]

S. Tan, D. Walls, and M. Collett, “Nonlocality of a single photon,” Phys. Rev. Lett. 66, 252–255 (1991).
[CrossRef]

1935 (1)

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935).
[CrossRef]

Aoki, T.

T. Aoki, N. Takey, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, and P. van Loock, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404–080407 (2003).
[CrossRef]

Barrett, S. D.

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]

Beausoleil, R. G.

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]

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, 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. Crepeau, 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]

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]

Bergou, J. A.

B. He, Y. Ren, and J. A. Bergou, “Creation of high-quality long-distance entanglement with flexible resources,” Phys. Rev. A 79, 052323 (2009).
[CrossRef]

B. He and J. A. Bergou, “Entanglement transformation with no classical communication,” Phys. Rev. A 78, 062328 (2008).
[CrossRef]

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F. G. Deng, C. Y. Li, Y. S. Li, H. Y. Zhou, and Y. Wang, “Symmetric multiparty-controlled teleportation of an arbitrary two-particle entanglement,” Phys. Rev. A 72, 022338 (2005).
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F. G. Deng, C. Y. Li, Y. S. Li, H. Y. Zhou, and Y. Wang, “Symmetric multiparty-controlled teleportation of an arbitrary two-particle entanglement,” Phys. Rev. A 72, 022338 (2005).
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B. He, Q. Lin, and C. Simon, “Cross-Kerr nonlinearity between continuous-mode coherent states and single photons,” Phys. Rev. A 83, 053826 (2011).
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C. Wang, F. G. Deng, Y. S. Li, X. S. Liu, and G. L. Long, “Quantum secure direct communication with high-dimension quantum superdense coding,” Phys. Rev. A 71, 044305 (2005).
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C. Wang, F. G. Deng, Y. S. Li, X. S. Liu, and G. L. Long, “Quantum secure direct communication with high-dimension quantum superdense coding,” Phys. Rev. A 71, 044305 (2005).
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C. Silberhorn, T. C. Ralph, N. Lütkenhaus, and G. Leuchs, “Continuous variable quantum cryptography: beating the 3 dB loss limit,” Phys. Rev. Lett. 89, 167901–167904 (2002).
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O. Göckl, S. Lorenz, C. Marquardt, J. Heersink, M. Brownnutt, C. Silberhorn, Q. Pan, P. van Loock, N. Korolkova, and G. Leuchs, “Experiment towards continuous-variable entanglement swapping: highly correlated four-partite quantum state,” Phys. Rev. A 68, 012319 (2003).
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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).
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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).
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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).
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M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).

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C. I. Osorio, N. Bruno, N. Sangouard, H. Zbinden, N. Gisin, and R. T. Thew, “Heralded photon amplification for quantum communication,” Phys. Rev. A 86, 023815 (2012).
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O. Göckl, S. Lorenz, C. Marquardt, J. Heersink, M. Brownnutt, C. Silberhorn, Q. Pan, P. van Loock, N. Korolkova, and G. Leuchs, “Experiment towards continuous-variable entanglement swapping: highly correlated four-partite quantum state,” Phys. Rev. A 68, 012319 (2003).
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M. G. A. Paris, M. Cola, and R. Bonifacio, “Quantum state engeneering assisted by entanglement,” Phys. Rev. A 67, 042104 (2003).
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G. M. D’Ariano, P. Lo Presti, and M. G. A. Paris, “Using entanglement improves the precision of quantum measurements,” Phys. Rev. Lett. 87, 270404–270407 (2001).
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Peng, K.

J. Jing, J. Zhang, Y. Yan, F. Zhao, C. Xie, and K. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90, 167903–167906 (2003).
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A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935).
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A. Furusawa, J. L. Søensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
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C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046–2052 (1996).
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C. Silberhorn, T. C. Ralph, N. Lütkenhaus, and G. Leuchs, “Continuous variable quantum cryptography: beating the 3 dB loss limit,” Phys. Rev. Lett. 89, 167901–167904 (2002).
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M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
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Ren, Y.

B. He, Y. Ren, and J. A. Bergou, “Creation of high-quality long-distance entanglement with flexible resources,” Phys. Rev. A 79, 052323 (2009).
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N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
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A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935).
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C. I. Osorio, N. Bruno, N. Sangouard, H. Zbinden, N. Gisin, and R. T. Thew, “Heralded photon amplification for quantum communication,” Phys. Rev. A 86, 023815 (2012).
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L. Heaney, A. Cabello, M. F. Santos, and V. Vedral, “Extreme nonlocality with one photon,” New J. Phys. 13, 053054–053065(2011).
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Schumacher, B.

C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046–2052 (1996).
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A. SenDe, U. Sen, M. Wieśniak, D. Kaszlikowski, and M. Żukowski, “Multiqubit W states lead to stronger nonclassicality than Greenberger-Horne-Zeilinger states,” Phys. Rev. A 68, 062306 (2003).
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Y. B. Sheng, L. Zhou, and S. M. Zhao, “Efficient two-step entanglement concentration for arbitrary W states,” Phys. Rev. A 85, 044302 (2012).
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Y. B. Sheng, L. Zhou, S. M. Zhao, and B. Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A 85, 012307 (2012).
[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).
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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).
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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).
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Ch. Silberhorn, N. Korolkova, and G. Leuchs, “Quantum key distribution with bright entangled beams,” Phys. Rev. Lett. 88, 167902–167905 (2002).
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B. He, Q. Lin, and C. Simon, “Cross-Kerr nonlinearity between continuous-mode coherent states and single photons,” Phys. Rev. A 83, 053826 (2011).
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H. F. Wang, L. L. Sun, S. Zhang, and K. H. Yeon, “Scheme for entanglement concentration of unknown partially entangled three-atom W states in cavity QED,” Quantum Inf. Process. 11, 431–441 (2012).
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N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
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O. Göckl, S. Lorenz, C. Marquardt, J. Heersink, M. Brownnutt, C. Silberhorn, Q. Pan, P. van Loock, N. Korolkova, and G. Leuchs, “Experiment towards continuous-variable entanglement swapping: highly correlated four-partite quantum state,” Phys. Rev. A 68, 012319 (2003).
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T. Aoki, N. Takey, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, and P. van Loock, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404–080407 (2003).
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S. Tan, D. Walls, and M. Collett, “Nonlocality of a single photon,” Phys. Rev. Lett. 66, 252–255 (1991).
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J. Jing, J. Zhang, Y. Yan, F. Zhao, C. Xie, and K. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90, 167903–167906 (2003).
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C. Wang, Y. Zhang, and G. S. Jin, “Polarization-entanglement purification and concentration using cross-Kerr nonlinearity,” Quantum Inf. Comput. 11, 988–1002 (2011).

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J. Jing, J. Zhang, Y. Yan, F. Zhao, C. Xie, and K. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90, 167903–167906 (2003).
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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).

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A. Yildiz, “Optimal distillation of three-qubit W states,” Phys. Rev. A 82, 012317 (2010).
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J. Jing, J. Zhang, Y. Yan, F. Zhao, C. Xie, and K. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90, 167903–167906 (2003).
[CrossRef]

T. Aoki, N. Takey, H. Yonezawa, K. Wakui, T. Hiraoka, A. Furusawa, and P. van Loock, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404–080407 (2003).
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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).

Quantum Inf. Process. (1)

H. F. Wang, L. L. Sun, S. Zhang, and K. H. Yeon, “Scheme for entanglement concentration of unknown partially entangled three-atom W states in cavity QED,” Quantum Inf. Process. 11, 431–441 (2012).
[CrossRef]

Rev. Mod. Phys. (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
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Science (1)

A. Furusawa, J. L. Søensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional quantum teleportation,” Science 282, 706–709 (1998).
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Figures (3)

Fig. 1.
Fig. 1.

Schematic drawing of the photon-number QND based on the weak cross-Kerr nonlinearity. Here, the photons in the spatial modes a1 and a2 pass through the cross-Kerr material. A photon in mode a1 can cause the phase shift of θ on the coherent state |αp, while a photon in mode a2 can cause the phase shift of θ. The phase shift can be determined with a momentum quadrature measurement, so that the photon number in the modes a1 and a2 can be checked without destroying the photons.

Fig. 2.
Fig. 2.

Schematic drawing of our ECP for distilling the maximally entangled single-photon W state from arbitrary single-photon less-entangled W state. The protocol includes two similar steps. In each concentration step, only a conventional auxiliary photon is needed to complete the task. In both steps, the QND is adopted to carry out the nondestructive photon-number measurement. The VBS is used to adjust the coefficients of the entangled state and ultimately obtain the maximally entangled state [58]. Moreover, with the help of the QND and VBS, the protocol can be used repeatedly to get a high success probability.

Fig. 3.
Fig. 3.

Success probability (Ptotal) of the concentration protocol for obtaining a maximally entangled single-photon three-mode W state. We make γ=(1)/(3) and α[0,(2)/(3)]. For numerical simulation, we suppose that both the two concentration steps are operated N times. Here, the three curves represent the relationship between the Ptotal and α under the conditions that N=1, 3, 5, respectively. It can be found that Ptotal largely depends on the initial coefficient α. Moreover, it is obvious that by repeating the protocol, the success probability can be largely increased.

Equations (43)

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

|ϕAB=12(|0A|1B+|1A|0B),
|WN=1N(|1,0,0,,0+|0,1,0,,0++|0,0,1),
|WN=a1|1,0,0,,0+a2|0,1,0,,0++aN|0,0,1,
Hck=χna^nb^,
Uck|ψ|α=(γ|0+δ|1)|αγ|0|α+δ|1|αeiθ.
|ψa1b1c1=α|1,0,0a1b1c1+β|0,1,0a1b1c1+γ|0,0,1a1b1c1.
|ψd1d2=1t|1,0d1d2+t|0,1d1d2.
|Ψa1b1c1d1d2=|ψa1b1c1|ψd1d2=(α1t|1,0,0,1,0+αt|1,0,0,0,1+β1t|0,1,0,1,0+βt|0,1,0,0,1+γ1t|0,0,1,1,0+γt|0,0,1,0,1)a1b1c1d1d2.
|Ψa1b1c1d1d2|αα1t|1,0,0,1,0a1b1c1d1d2|αeiθ+αt|1,0,0,0,1a1b1c1d1d2|α+β1t|0,1,0,1,0a1b1c1d1d2|α+βt|0,1,0,0,1a1b1c1d1d2|αeiθ+γ1t|0,0,1,1,0a1b1c1d1d2|αeiθ+γt|0,0,1,0,1a1b1c1d1d2|α.
|Ψ1a1b1c1d1d2=α1t|1,0,0,1,0a1b1c1d1d2+βt|0,1,0,0,1a1b1c1d1d2+γ1t|0,0,1,1,0a1b1c1d1d2.
d^1|0=12(e^1|0+e^2|0),d^2|0=12(e^1|0e^2|0).
|Ψ1a1b1c1e1e2=(α1t2|1,0,0a1b1c1+βt2|0,1,0a1b1c1+γ1t2|0,0,1a1b1c1)|1e1+(α1t2|1,0,0a1b1c1βt2|0,1,0a1b1c1+γ1t2|0,0,1a1b1c1)|1e2.
|ψ1a1b1c1=α1t|1,0,0a1b1c1+βt|0,1,0a1b1c1+γ1t|0,0,1a1b1c1,
|ψ1a1b1c1=α1t|1,0,0a1b1c1βt|0,1,0a1b1c1+γ1t|0,0,1a1b1c1.
|ψ1a1b1c1=αβα2+β2|1,0,0a1b1c1+αβα2+β2|0,1,0a1b1c1+γβα2+β2|0,0,1a1b1c1,
|ψ1a1b1c1=α|1,0,0a1b1c1+α|0,1,0a1b1c1+γ|0,0,1a1b1c1.
P11=|β|2(2|α|2+|γ|2)|α|2+|β|2.
|Ψa1b1c1d1d2=α2|1,0,0,0,1a1b1c1d1d2+β2|0,1,0,1,0a1b1c1d1d2+αγ|0,0,1,0,1a1b1c1d1d2.
|ψ2a1b1c1=α2|1,0,0a1b1c1+β2|0,1,0a1b1c1+αγ|0,0,1a1b1c1,
|ψ2a1b1c1=α2|1,0,0a1b1c1β2|0,1,0a1b1c1+αγ|0,0,1a1b1c1.
|ψ2a1b1c1=α2α4+β4+α2γ2|1,0,0a1b1c1+β2α4+β4+α2γ2|0,1,0a1b1c1+αγα4+β4+α2γ2|0,0,1a1b1c1.
|ψ3a1b1c1=α21t12|1,0,0a1b1c1+β2t12|0,1,0a1b1c1+αγ1t12|0,0,1a1b1c1.
P12=|β|4(|αγ|2+2|α|4)(|α|2+|β|2)(|α|4+|β|4).
|ψ4a1b1c1=α4|1,0,0a1b1c1+β4|0,1,0a1b1c1+α3γ|0,0,1a1b1c1,
P1K=|β|2K(|α|2K2|γ|2+2|α|2K)(|α|2+|β|2)(|α|4+|β|4)(|α|2K+|β|2K),
Ptotal1=P11+P12++P1K=K=1P1K.
|ψg1g2=1t2|1,0g1g2+t2|0,1g1g2.
|ψ1a1b1c1|ψg1g2|αα1t2|1,0,0,1,0a1b1c1g1g2|αeiθ+αt2|1,0,0,0,1a1b1c1g1g2|α+α1t2|0,1,0,1,0a1b1c1g1g2|αeiθ+αt2|0,1,0,0,1a1b1c1g1g2|α+γ1t2|0,0,1,1,0a1b1c1g1g2|α+γt2|0,0,1,0,1a1b1c1g1g2|αeiθ.
|Ψ2a1b1c1g1g2=α1t2|1,0,0,1,0a1b1c1g1g2+α1t2|0,1,0,1,0a1b1c1g1g2+γt2|0,0,1,0,1a1b1c1g1g2.
g^1|0=12(f^1|0+f^2|0),g^2|0=12(f^1|0f^2|0).
|Ψ2a1b1c1f1f2=(α1t2|1,0,0+α1t2|0,1,0+γt2|0,0,1)a1b1c1|1f1+(α1t2|1,0,0+α1t2|0,1,0γt2|0,0,1)a1b1c1|1f2.
|ψ5a1b1c1=α1t2|1,0,0a1b1c1+α1t2|0,1,0a1b1c1+γt2|0,0,1a1b1c1,
|ψ5a1b1c1=α1t2|1,0,0a1b1c1+α1t2|0,1,0a1b1c1γt2|0,0,1a1b1c1.
|ψ5a1b1c1=13(|1,0,0a1b1c1+|0,1,0a1b1c1+|0,0,1a1b1c1),
P21=3|α|2|γ|2(|α|2+|γ|2)(2|α|2+|γ|2),
|Ψ2a1b1c1g1g2=α2|1,0,0,0,1a1b1c1g1g2+α2|0,1,0,0,1a1b1c1g1g2+γ2|0,0,1,1,0a1b1c1g1g2.
|ψ6a1b1c1=α2|1,0,0a1b1c1+α2|0,1,0a1b1c1+γ2|0,0,1a1b1c1.
|ψ7a1b1c1=α21t22|1,0,0a1b1c1+α21t22|0,1,0a1b1c1+γ2t22|0,0,1a1b1c1.
P22=3|α|4|γ|4(|α|2+|γ|2)(|α|4+|γ|4)(2|α|2+|γ|2).
|ψ8a1b1c1=α4|1,0,0a1b1c1+α4|0,1,0a1b1c1+γ4|0,0,1a1b1c1,
P2K=3|α|2K|γ|2K(|α|2+|γ|2)(|α|4+|γ|4)(|α|2K+|γ|2K)(2|α|2+|γ|2).
Ptotal2=P21+P22++P2K=K=1P2K.
Ptotal=Ptotal1Ptotal2=K=1P1KK=1P2K.

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