Abstract

We propose two experimental schemes for concentrating entanglement in unknown partially entangled three-photon W states with only linear optical elements and the conventional photon detectors. We first propose a heralded scheme using a heralded controlled-NOT (CNOT) gate between two photons. Then we simplify this method to a post-selected one requiring time entanglement of the input photons without using ancillary photons. In the two schemes, Alice, Bob, and Charlie at three distant parties can obtain one maximally entangled three-photon W state from two identical partially entangled three-photon W states, taking the specific form of α|H|H|V+β(|H|V|H+|V|H|H), by local operations and classical communication. We discuss and consider the success probabilities and the practical realizations of the schemes.

© 2010 Optical Society of America

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    [CrossRef] [PubMed]
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  7. 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).
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    [CrossRef] [PubMed]
  29. S. Gasparoni, J. W. Pan, P. Walther, T. Rudolph, and A. Zeilinger, “Realization of a photonic controlled-NOT gate sufficient for quantum computation,” Phys. Rev. Lett. 93, 020504 (2004).
    [CrossRef] [PubMed]
  30. R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, “Demonstration of an optical quantum controlled-NOT gate without path interference,” Phys. Rev. Lett. 95, 210506 (2005).
    [CrossRef] [PubMed]
  31. Z. Zhao, A. N. Zhang, Y. A. Chen, H. Zhang, J. F. Du, T. Yang, and J. W. Pan, “Experimental demonstration of a nondestructive controlled-NOT quantum gate for two independent photon qubits,” Phys. Rev. Lett. 94, 030501 (2005).
    [CrossRef] [PubMed]
  32. N. Kiesel, Ch. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210505 (2005).
    [CrossRef] [PubMed]
  33. N. K. Langford, T. J. Weinhold, R. Prevedel, A. Gilchrist, J. L. O’Brien, G. J. Pryde, and A. G. White, “Demonstration of a simple entangling optical gate and its use in Bell-state analysis,” Phys. Rev. Lett. 95, 210504 (2005).
    [CrossRef] [PubMed]
  34. J. W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
    [CrossRef]
  35. M. Zukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, ““Event-ready-detectors” Bell experiment via entanglement swapping,” Phys. Rev. Lett. 71, 4287–4290 (1993).
    [CrossRef] [PubMed]
  36. O. Benson, C. Santori, M. Pelton, and Y. Yamamoto, “Regulated and entangled photons from a single quantum dot,” Phys. Rev. Lett. 84, 2513–2516 (2000).
    [CrossRef] [PubMed]
  37. N. Akopian, N. H. Lindner, E. Poem, Y. Berlatzky, J. Avron, D. Gershoni, B. D. Gerardot, and P. M. Petroff, “Entangled photon pairs from semiconductor quantum dots,” Phys. Rev. Lett. 96, 130501 (2006).
    [CrossRef] [PubMed]

2007 (1)

X. B. Zou, S. L. Zhang, K. Li, and G. C. Guo, “Linear optical implementation of the two-qubit controlled phase gate with conventional photon detectors,” Phys. Rev. A 75, 034302 (2007).
[CrossRef]

2006 (3)

X. B. Zou, K. Li, and G. C. Guo, “Linear optical scheme for direct implementation of a nondestructive N-qubit controlled phase gate,” Phys. Rev. A 74, 044305 (2006).
[CrossRef]

N. Akopian, N. H. Lindner, E. Poem, Y. Berlatzky, J. Avron, D. Gershoni, B. D. Gerardot, and P. M. Petroff, “Entangled photon pairs from semiconductor quantum dots,” Phys. Rev. Lett. 96, 130501 (2006).
[CrossRef] [PubMed]

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]

2005 (5)

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]

R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, “Demonstration of an optical quantum controlled-NOT gate without path interference,” Phys. Rev. Lett. 95, 210506 (2005).
[CrossRef] [PubMed]

Z. Zhao, A. N. Zhang, Y. A. Chen, H. Zhang, J. F. Du, T. Yang, and J. W. Pan, “Experimental demonstration of a nondestructive controlled-NOT quantum gate for two independent photon qubits,” Phys. Rev. Lett. 94, 030501 (2005).
[CrossRef] [PubMed]

N. Kiesel, Ch. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210505 (2005).
[CrossRef] [PubMed]

N. K. Langford, T. J. Weinhold, R. Prevedel, A. Gilchrist, J. L. O’Brien, G. J. Pryde, and A. G. White, “Demonstration of a simple entangling optical gate and its use in Bell-state analysis,” Phys. Rev. Lett. 95, 210504 (2005).
[CrossRef] [PubMed]

2004 (2)

S. Gasparoni, J. W. Pan, P. Walther, T. Rudolph, and A. Zeilinger, “Realization of a photonic controlled-NOT gate sufficient for quantum computation,” Phys. Rev. Lett. 93, 020504 (2004).
[CrossRef] [PubMed]

F. G. Deng and G. L. Long, “Bidirectional quantum key distribution protocol with practical faint laser pulses,” Phys. Rev. A 70, 012311 (2004).
[CrossRef]

2003 (3)

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]

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]

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature 426, 264–267 (2003).
[CrossRef] [PubMed]

2002 (2)

K. Sanaka, K. Kawahara, and T. Kuga, “Experimental probabilistic manipulation of down-converted photon pairs using unbalanced interferometers,” Phys. Rev. A 66, 040301(R) (2002).
[CrossRef]

X. B. Zou, K. Pahlke, and W. Mathis, “Generation of an entangled four-photon W state,” Phys. Rev. A 66, 044302 (2002).
[CrossRef]

2001 (7)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef] [PubMed]

M. Koashi, T. Yamamoto, and N. Imoto, “Probabilistic manipulation of entangled photons,” Phys. Rev. A 63, 030301(R) (2001).
[CrossRef]

T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Probabilistic quantum logic operations using polarizing beam splitters,” Phys. Rev. A 64, 062311 (2001).
[CrossRef]

J. W. Pan, C. Simon, C. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature 410, 1067–1070 (2001).
[CrossRef] [PubMed]

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]

H. K. Lo and S. Popescu, “Concentrating entanglement by local actions: beyond mean values,” Phys. Rev. A 63, 022301 (2001).
[CrossRef]

2000 (3)

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

P. Kok and S. L. Braunstein, “Postselected versus nonpostselected quantum teleportation using parametric down-conversion,” Phys. Rev. A 61, 042304 (2000).
[CrossRef]

O. Benson, C. Santori, M. Pelton, and Y. Yamamoto, “Regulated and entangled photons from a single quantum dot,” Phys. Rev. Lett. 84, 2513–2516 (2000).
[CrossRef] [PubMed]

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 (1)

J. W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
[CrossRef]

1997 (1)

N. Gisin and S. Massar, “Optimal quantum cloning machines,” Phys. Rev. Lett. 79, 2153–2156 (1997).
[CrossRef]

1996 (4)

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]

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]

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]

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]

1993 (2)

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] [PubMed]

M. Zukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, ““Event-ready-detectors” Bell experiment via entanglement swapping,” Phys. Rev. Lett. 71, 4287–4290 (1993).
[CrossRef] [PubMed]

1991 (1)

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

Akopian, N.

N. Akopian, N. H. Lindner, E. Poem, Y. Berlatzky, J. Avron, D. Gershoni, B. D. Gerardot, and P. M. Petroff, “Entangled photon pairs from semiconductor quantum dots,” Phys. Rev. Lett. 96, 130501 (2006).
[CrossRef] [PubMed]

Avron, J.

N. Akopian, N. H. Lindner, E. Poem, Y. Berlatzky, J. Avron, D. Gershoni, B. D. Gerardot, and P. M. Petroff, “Entangled photon pairs from semiconductor quantum dots,” Phys. Rev. Lett. 96, 130501 (2006).
[CrossRef] [PubMed]

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] [PubMed]

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]

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]

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] [PubMed]

Benson, O.

O. Benson, C. Santori, M. Pelton, and Y. Yamamoto, “Regulated and entangled photons from a single quantum dot,” Phys. Rev. Lett. 84, 2513–2516 (2000).
[CrossRef] [PubMed]

Berlatzky, Y.

N. Akopian, N. H. Lindner, E. Poem, Y. Berlatzky, J. Avron, D. Gershoni, B. D. Gerardot, and P. M. Petroff, “Entangled photon pairs from semiconductor quantum dots,” Phys. Rev. Lett. 96, 130501 (2006).
[CrossRef] [PubMed]

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] [PubMed]

Bose, S.

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

Bouwmeester, D.

J. W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
[CrossRef]

Branning, D.

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature 426, 264–267 (2003).
[CrossRef] [PubMed]

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] [PubMed]

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] [PubMed]

Braunstein, S. L.

P. Kok and S. L. Braunstein, “Postselected versus nonpostselected quantum teleportation using parametric down-conversion,” Phys. Rev. A 61, 042304 (2000).
[CrossRef]

Brukner, C.

J. W. Pan, C. Simon, C. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature 410, 1067–1070 (2001).
[CrossRef] [PubMed]

Cao, Z. L.

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]

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]

Chen, Y. A.

Z. Zhao, A. N. Zhang, Y. A. Chen, H. Zhang, J. F. Du, T. Yang, and J. W. Pan, “Experimental demonstration of a nondestructive controlled-NOT quantum gate for two independent photon qubits,” Phys. Rev. Lett. 94, 030501 (2005).
[CrossRef] [PubMed]

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]

Cirac, J. I.

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

Crepeau, C.

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] [PubMed]

Deng, F. G.

F. G. Deng and G. L. Long, “Bidirectional quantum key distribution protocol with practical faint laser pulses,” Phys. Rev. A 70, 012311 (2004).
[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] [PubMed]

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] [PubMed]

Du, J. F.

Z. Zhao, A. N. Zhang, Y. A. Chen, H. Zhang, J. F. Du, T. Yang, and J. W. Pan, “Experimental demonstration of a nondestructive controlled-NOT quantum gate for two independent photon qubits,” Phys. Rev. Lett. 94, 030501 (2005).
[CrossRef] [PubMed]

Dür, W.

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

Ekert, A. K.

M. Zukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, ““Event-ready-detectors” Bell experiment via entanglement swapping,” Phys. Rev. Lett. 71, 4287–4290 (1993).
[CrossRef] [PubMed]

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

Franson, J. D.

T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Probabilistic quantum logic operations using polarizing beam splitters,” Phys. Rev. A 64, 062311 (2001).
[CrossRef]

Gasparoni, S.

S. Gasparoni, J. W. Pan, P. Walther, T. Rudolph, and A. Zeilinger, “Realization of a photonic controlled-NOT gate sufficient for quantum computation,” Phys. Rev. Lett. 93, 020504 (2004).
[CrossRef] [PubMed]

Gerardot, B. D.

N. Akopian, N. H. Lindner, E. Poem, Y. Berlatzky, J. Avron, D. Gershoni, B. D. Gerardot, and P. M. Petroff, “Entangled photon pairs from semiconductor quantum dots,” Phys. Rev. Lett. 96, 130501 (2006).
[CrossRef] [PubMed]

Gershoni, D.

N. Akopian, N. H. Lindner, E. Poem, Y. Berlatzky, J. Avron, D. Gershoni, B. D. Gerardot, and P. M. Petroff, “Entangled photon pairs from semiconductor quantum dots,” Phys. Rev. Lett. 96, 130501 (2006).
[CrossRef] [PubMed]

Gilchrist, A.

N. K. Langford, T. J. Weinhold, R. Prevedel, A. Gilchrist, J. L. O’Brien, G. J. Pryde, and A. G. White, “Demonstration of a simple entangling optical gate and its use in Bell-state analysis,” Phys. Rev. Lett. 95, 210504 (2005).
[CrossRef] [PubMed]

Gisin, N.

N. Gisin and S. Massar, “Optimal quantum cloning machines,” Phys. Rev. Lett. 79, 2153–2156 (1997).
[CrossRef]

Guo, G. C.

X. B. Zou, S. L. Zhang, K. Li, and G. C. Guo, “Linear optical implementation of the two-qubit controlled phase gate with conventional photon detectors,” Phys. Rev. A 75, 034302 (2007).
[CrossRef]

X. B. Zou, K. Li, and G. C. Guo, “Linear optical scheme for direct implementation of a nondestructive N-qubit controlled phase gate,” Phys. Rev. A 74, 044305 (2006).
[CrossRef]

Hofmann, H. F.

R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, “Demonstration of an optical quantum controlled-NOT gate without path interference,” Phys. Rev. Lett. 95, 210506 (2005).
[CrossRef] [PubMed]

Horne, M. A.

M. Zukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, ““Event-ready-detectors” Bell experiment via entanglement swapping,” Phys. Rev. Lett. 71, 4287–4290 (1993).
[CrossRef] [PubMed]

Imoto, N.

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]

M. Koashi, T. Yamamoto, and N. Imoto, “Probabilistic manipulation of entangled photons,” Phys. Rev. A 63, 030301(R) (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]

Jacobs, B. C.

T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Probabilistic quantum logic operations using polarizing beam splitters,” Phys. Rev. A 64, 062311 (2001).
[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] [PubMed]

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] [PubMed]

Kawahara, K.

K. Sanaka, K. Kawahara, and T. Kuga, “Experimental probabilistic manipulation of down-converted photon pairs using unbalanced interferometers,” Phys. Rev. A 66, 040301(R) (2002).
[CrossRef]

Kiesel, N.

N. Kiesel, Ch. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210505 (2005).
[CrossRef] [PubMed]

Knight, P. L.

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

Knill, E.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef] [PubMed]

Koashi, M.

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]

M. Koashi, T. Yamamoto, and N. Imoto, “Probabilistic manipulation of entangled photons,” Phys. Rev. A 63, 030301(R) (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]

Kok, P.

P. Kok and S. L. Braunstein, “Postselected versus nonpostselected quantum teleportation using parametric down-conversion,” Phys. Rev. A 61, 042304 (2000).
[CrossRef]

Kuga, T.

K. Sanaka, K. Kawahara, and T. Kuga, “Experimental probabilistic manipulation of down-converted photon pairs using unbalanced interferometers,” Phys. Rev. A 66, 040301(R) (2002).
[CrossRef]

Laflamme, R.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef] [PubMed]

Langford, N. K.

N. K. Langford, T. J. Weinhold, R. Prevedel, A. Gilchrist, J. L. O’Brien, G. J. Pryde, and A. G. White, “Demonstration of a simple entangling optical gate and its use in Bell-state analysis,” Phys. Rev. Lett. 95, 210504 (2005).
[CrossRef] [PubMed]

Li, K.

X. B. Zou, S. L. Zhang, K. Li, and G. C. Guo, “Linear optical implementation of the two-qubit controlled phase gate with conventional photon detectors,” Phys. Rev. A 75, 034302 (2007).
[CrossRef]

X. B. Zou, K. Li, and G. C. Guo, “Linear optical scheme for direct implementation of a nondestructive N-qubit controlled phase gate,” Phys. Rev. A 74, 044305 (2006).
[CrossRef]

Lindner, N. H.

N. Akopian, N. H. Lindner, E. Poem, Y. Berlatzky, J. Avron, D. Gershoni, B. D. Gerardot, and P. M. Petroff, “Entangled photon pairs from semiconductor quantum dots,” Phys. Rev. Lett. 96, 130501 (2006).
[CrossRef] [PubMed]

Lo, H. K.

H. K. Lo and S. Popescu, “Concentrating entanglement by local actions: beyond mean values,” Phys. Rev. A 63, 022301 (2001).
[CrossRef]

Long, G. L.

F. G. Deng and G. L. Long, “Bidirectional quantum key distribution protocol with practical faint laser pulses,” Phys. Rev. A 70, 012311 (2004).
[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] [PubMed]

Massar, S.

N. Gisin and S. Massar, “Optimal quantum cloning machines,” Phys. Rev. Lett. 79, 2153–2156 (1997).
[CrossRef]

Mathis, W.

X. B. Zou, K. Pahlke, and W. Mathis, “Generation of an entangled four-photon W state,” Phys. Rev. A 66, 044302 (2002).
[CrossRef]

Milburn, G. J.

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef] [PubMed]

O’Brien, J. L.

N. K. Langford, T. J. Weinhold, R. Prevedel, A. Gilchrist, J. L. O’Brien, G. J. Pryde, and A. G. White, “Demonstration of a simple entangling optical gate and its use in Bell-state analysis,” Phys. Rev. Lett. 95, 210504 (2005).
[CrossRef] [PubMed]

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature 426, 264–267 (2003).
[CrossRef] [PubMed]

Okamoto, R.

R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, “Demonstration of an optical quantum controlled-NOT gate without path interference,” Phys. Rev. Lett. 95, 210506 (2005).
[CrossRef] [PubMed]

Ozdemir, S. K.

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]

Pahlke, K.

X. B. Zou, K. Pahlke, and W. Mathis, “Generation of an entangled four-photon W state,” Phys. Rev. A 66, 044302 (2002).
[CrossRef]

Pan, J. W.

Z. Zhao, A. N. Zhang, Y. A. Chen, H. Zhang, J. F. Du, T. Yang, and J. W. Pan, “Experimental demonstration of a nondestructive controlled-NOT quantum gate for two independent photon qubits,” Phys. Rev. Lett. 94, 030501 (2005).
[CrossRef] [PubMed]

S. Gasparoni, J. W. Pan, P. Walther, T. Rudolph, and A. Zeilinger, “Realization of a photonic controlled-NOT gate sufficient for quantum computation,” Phys. Rev. Lett. 93, 020504 (2004).
[CrossRef] [PubMed]

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]

J. W. Pan, C. Simon, C. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature 410, 1067–1070 (2001).
[CrossRef] [PubMed]

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

J. W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
[CrossRef]

Pelton, M.

O. Benson, C. Santori, M. Pelton, and Y. Yamamoto, “Regulated and entangled photons from a single quantum dot,” Phys. Rev. Lett. 84, 2513–2516 (2000).
[CrossRef] [PubMed]

Peres, A.

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] [PubMed]

Petroff, P. M.

N. Akopian, N. H. Lindner, E. Poem, Y. Berlatzky, J. Avron, D. Gershoni, B. D. Gerardot, and P. M. Petroff, “Entangled photon pairs from semiconductor quantum dots,” Phys. Rev. Lett. 96, 130501 (2006).
[CrossRef] [PubMed]

Pittman, T. B.

T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Probabilistic quantum logic operations using polarizing beam splitters,” Phys. Rev. A 64, 062311 (2001).
[CrossRef]

Poem, E.

N. Akopian, N. H. Lindner, E. Poem, Y. Berlatzky, J. Avron, D. Gershoni, B. D. Gerardot, and P. M. Petroff, “Entangled photon pairs from semiconductor quantum dots,” Phys. Rev. Lett. 96, 130501 (2006).
[CrossRef] [PubMed]

Popescu, S.

H. K. Lo and S. Popescu, “Concentrating entanglement by local actions: beyond mean values,” Phys. Rev. A 63, 022301 (2001).
[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] [PubMed]

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]

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]

Prevedel, R.

N. K. Langford, T. J. Weinhold, R. Prevedel, A. Gilchrist, J. L. O’Brien, G. J. Pryde, and A. G. White, “Demonstration of a simple entangling optical gate and its use in Bell-state analysis,” Phys. Rev. Lett. 95, 210504 (2005).
[CrossRef] [PubMed]

Pryde, G. J.

N. K. Langford, T. J. Weinhold, R. Prevedel, A. Gilchrist, J. L. O’Brien, G. J. Pryde, and A. G. White, “Demonstration of a simple entangling optical gate and its use in Bell-state analysis,” Phys. Rev. Lett. 95, 210504 (2005).
[CrossRef] [PubMed]

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature 426, 264–267 (2003).
[CrossRef] [PubMed]

Ralph, T. C.

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature 426, 264–267 (2003).
[CrossRef] [PubMed]

Rudolph, T.

S. Gasparoni, J. W. Pan, P. Walther, T. Rudolph, and A. Zeilinger, “Realization of a photonic controlled-NOT gate sufficient for quantum computation,” Phys. Rev. Lett. 93, 020504 (2004).
[CrossRef] [PubMed]

Sanaka, K.

K. Sanaka, K. Kawahara, and T. Kuga, “Experimental probabilistic manipulation of down-converted photon pairs using unbalanced interferometers,” Phys. Rev. A 66, 040301(R) (2002).
[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] [PubMed]

Santori, C.

O. Benson, C. Santori, M. Pelton, and Y. Yamamoto, “Regulated and entangled photons from a single quantum dot,” Phys. Rev. Lett. 84, 2513–2516 (2000).
[CrossRef] [PubMed]

Sasaki, K.

R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, “Demonstration of an optical quantum controlled-NOT gate without path interference,” Phys. Rev. Lett. 95, 210506 (2005).
[CrossRef] [PubMed]

Schmid, Ch.

N. Kiesel, Ch. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210505 (2005).
[CrossRef] [PubMed]

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] [PubMed]

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]

Shi, B. S.

B. S. Shi and T. Tomita, “Schemes for generating W state of paths and W state of polarization photons,” ArXiv.org e-print, 0208170, 2002, http://arxiv.org/abs/quant-ph/0208170.

Simon, C.

J. W. Pan, C. Simon, C. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature 410, 1067–1070 (2001).
[CrossRef] [PubMed]

Smolin, J. A.

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]

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]

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]

Takeuchi, S.

R. Okamoto, H. F. Hofmann, S. Takeuchi, and K. Sasaki, “Demonstration of an optical quantum controlled-NOT gate without path interference,” Phys. Rev. Lett. 95, 210506 (2005).
[CrossRef] [PubMed]

Tomita, T.

B. S. Shi and T. Tomita, “Schemes for generating W state of paths and W state of polarization photons,” ArXiv.org e-print, 0208170, 2002, http://arxiv.org/abs/quant-ph/0208170.

Ursin, R.

N. Kiesel, Ch. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210505 (2005).
[CrossRef] [PubMed]

Vedral, V.

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

Vidal, G.

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

Walther, P.

S. Gasparoni, J. W. Pan, P. Walther, T. Rudolph, and A. Zeilinger, “Realization of a photonic controlled-NOT gate sufficient for quantum computation,” Phys. Rev. Lett. 93, 020504 (2004).
[CrossRef] [PubMed]

Weber, U.

N. Kiesel, Ch. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210505 (2005).
[CrossRef] [PubMed]

Weinfurter, H.

N. Kiesel, Ch. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made simple,” Phys. Rev. Lett. 95, 210505 (2005).
[CrossRef] [PubMed]

J. W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
[CrossRef]

Weinhold, T. J.

N. K. Langford, T. J. Weinhold, R. Prevedel, A. Gilchrist, J. L. O’Brien, G. J. Pryde, and A. G. White, “Demonstration of a simple entangling optical gate and its use in Bell-state analysis,” Phys. Rev. Lett. 95, 210504 (2005).
[CrossRef] [PubMed]

White, A. G.

N. K. Langford, T. J. Weinhold, R. Prevedel, A. Gilchrist, J. L. O’Brien, G. J. Pryde, and A. G. White, “Demonstration of a simple entangling optical gate and its use in Bell-state analysis,” Phys. Rev. Lett. 95, 210504 (2005).
[CrossRef] [PubMed]

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature 426, 264–267 (2003).
[CrossRef] [PubMed]

Wootters, W. K.

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]

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]

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] [PubMed]

Yamamoto, T.

M. Koashi, T. Yamamoto, and N. Imoto, “Probabilistic manipulation of entangled photons,” Phys. Rev. A 63, 030301(R) (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]

Yamamoto, Y.

O. Benson, C. Santori, M. Pelton, and Y. Yamamoto, “Regulated and entangled photons from a single quantum dot,” Phys. Rev. Lett. 84, 2513–2516 (2000).
[CrossRef] [PubMed]

Yamomoto, T.

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]

Yang, M.

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]

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]

Yang, T.

Z. Zhao, A. N. Zhang, Y. A. Chen, H. Zhang, J. F. Du, T. Yang, and J. W. Pan, “Experimental demonstration of a nondestructive controlled-NOT quantum gate for two independent photon qubits,” Phys. Rev. Lett. 94, 030501 (2005).
[CrossRef] [PubMed]

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]

Zeilinger, A.

S. Gasparoni, J. W. Pan, P. Walther, T. Rudolph, and A. Zeilinger, “Realization of a photonic controlled-NOT gate sufficient for quantum computation,” Phys. Rev. Lett. 93, 020504 (2004).
[CrossRef] [PubMed]

J. W. Pan, C. Simon, C. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature 410, 1067–1070 (2001).
[CrossRef] [PubMed]

J. W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
[CrossRef]

M. Zukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, ““Event-ready-detectors” Bell experiment via entanglement swapping,” Phys. Rev. Lett. 71, 4287–4290 (1993).
[CrossRef] [PubMed]

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, A. N. Zhang, Y. A. Chen, H. Zhang, J. F. Du, T. Yang, and J. W. Pan, “Experimental demonstration of a nondestructive controlled-NOT quantum gate for two independent photon qubits,” Phys. Rev. Lett. 94, 030501 (2005).
[CrossRef] [PubMed]

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]

Zhang, H.

Z. Zhao, A. N. Zhang, Y. A. Chen, H. Zhang, J. F. Du, T. Yang, and J. W. Pan, “Experimental demonstration of a nondestructive controlled-NOT quantum gate for two independent photon qubits,” Phys. Rev. Lett. 94, 030501 (2005).
[CrossRef] [PubMed]

Zhang, L. H.

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]

Zhang, S. L.

X. B. Zou, S. L. Zhang, K. Li, and G. C. Guo, “Linear optical implementation of the two-qubit controlled phase gate with conventional photon detectors,” Phys. Rev. A 75, 034302 (2007).
[CrossRef]

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, A. N. Zhang, Y. A. Chen, H. Zhang, J. F. Du, T. Yang, and J. W. Pan, “Experimental demonstration of a nondestructive controlled-NOT quantum gate for two independent photon qubits,” Phys. Rev. Lett. 94, 030501 (2005).
[CrossRef] [PubMed]

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]

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

Zou, X. B.

X. B. Zou, S. L. Zhang, K. Li, and G. C. Guo, “Linear optical implementation of the two-qubit controlled phase gate with conventional photon detectors,” Phys. Rev. A 75, 034302 (2007).
[CrossRef]

X. B. Zou, K. Li, and G. C. Guo, “Linear optical scheme for direct implementation of a nondestructive N-qubit controlled phase gate,” Phys. Rev. A 74, 044305 (2006).
[CrossRef]

X. B. Zou, K. Pahlke, and W. Mathis, “Generation of an entangled four-photon W state,” Phys. Rev. A 66, 044302 (2002).
[CrossRef]

Zukowski, M.

M. Zukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, ““Event-ready-detectors” Bell experiment via entanglement swapping,” Phys. Rev. Lett. 71, 4287–4290 (1993).
[CrossRef] [PubMed]

Nature (4)

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]

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, “Demonstration of an all-optical quantum controlled-NOT gate,” Nature 426, 264–267 (2003).
[CrossRef] [PubMed]

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409, 46–52 (2001).
[CrossRef] [PubMed]

J. W. Pan, C. Simon, C. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature 410, 1067–1070 (2001).
[CrossRef] [PubMed]

Phys. Rev. A (17)

P. Kok and S. L. Braunstein, “Postselected versus nonpostselected quantum teleportation using parametric down-conversion,” Phys. Rev. A 61, 042304 (2000).
[CrossRef]

M. Koashi, T. Yamamoto, and N. Imoto, “Probabilistic manipulation of entangled photons,” Phys. Rev. A 63, 030301(R) (2001).
[CrossRef]

X. B. Zou, K. Li, and G. C. Guo, “Linear optical scheme for direct implementation of a nondestructive N-qubit controlled phase gate,” Phys. Rev. A 74, 044305 (2006).
[CrossRef]

T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Probabilistic quantum logic operations using polarizing beam splitters,” Phys. Rev. A 64, 062311 (2001).
[CrossRef]

X. B. Zou, S. L. Zhang, K. Li, and G. C. Guo, “Linear optical implementation of the two-qubit controlled phase gate with conventional photon detectors,” Phys. Rev. A 75, 034302 (2007).
[CrossRef]

K. Sanaka, K. Kawahara, and T. Kuga, “Experimental probabilistic manipulation of down-converted photon pairs using unbalanced interferometers,” Phys. Rev. A 66, 040301(R) (2002).
[CrossRef]

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

X. B. Zou, K. Pahlke, and W. Mathis, “Generation of an entangled four-photon W state,” Phys. Rev. A 66, 044302 (2002).
[CrossRef]

F. G. Deng and G. L. Long, “Bidirectional quantum key distribution protocol with practical faint laser pulses,” Phys. Rev. A 70, 012311 (2004).
[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] [PubMed]

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]

H. K. Lo and S. Popescu, “Concentrating entanglement by local actions: beyond mean values,” Phys. Rev. A 63, 022301 (2001).
[CrossRef]

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

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of generating an entangled four-photon W state proposed in [19]. PBS i denote polarization beam splitters, BS i are beam splitters, EPR denotes the two-photon entangled state ( | H 1 | V 2 + | V 1 | H 2 ) 2 , and D j are detectors.

Fig. 2
Fig. 2

Schematic diagram of the proposed heralded entanglement concentration scheme. PBS i denote polarization beam splitters, R 90 denotes HWP, and D b i j are detectors.

Fig. 3
Fig. 3

Schematic diagram for realizing the CNOT gate given in [27]. The target photon is split along the short ( t S ) or long ( t L ) path at the first beam splitter BS 1 and combined again in the same path at BS 2 , and the control photon is split along the short ( c S ) or long ( c L ) path at PBS 1 and combined again in the same path at PBS 2 . Here BS i are balanced beam splitter, PBS j denote polarization beam splitters, and R 90 denotes HWP.

Fig. 4
Fig. 4

Schematic diagram of the proposed post-selected entanglement concentration scheme. Here PBS i denote polarization beam splitters, BS j are balanced beam splitter, R 90 denotes HWP, and D b m k are detectors.

Equations (22)

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| ϕ 123 = α | H 1 | H 2 | V 3 + β ( | H 1 | V 2 | H 3 + | V 1 | H 2 | H 3 ) ,
| ϕ 456 = α | H 4 | H 5 | V 6 + β ( | H 4 | V 5 | H 6 + | V 4 | H 5 | H 6 ) ,
| Ψ s = ( | H 4 | H 2 | H 3 | V 1 + | H 4 | H 2 | V 3 | H 1 ) 2 + ( | V 4 | H 2 | H 3 | H 1 + | H 4 | V 2 | H 3 | H 1 ) 2 .
| Ψ d = μ ( | H 4 | H 2 | H 3 | V 1 + | H 4 | H 2 | V 3 | H 1 ) + ν ( | V 4 | H 2 | H 3 | H 1 + | H 4 | V 2 | H 3 | H 1 ) .
| Ψ d = δ | H 4 | H 2 | V 3 + γ ( | H 4 | V 2 | H 3 + | V 4 | H 2 | H 3 ) .
| H i 1 2 ( | H i + | V i ) ,
| V i 1 2 ( | H i | V i ) ,
| Ψ = α 2 | H 1 | V 2 | V 3 | H 4 | H 5 | V 6 + α β ( | H 1 | H 2 | V 3 | H 4 | V 5 | H 6 + | H 1 | H 2 | V 3 | V 4 | H 5 | H 6 + | H 1 | H 2 | H 3 | H 4 | H 5 | V 6 + | V 1 | V 2 | H 3 | H 4 | H 5 | V 6 ) + β 2 ( | H 1 | V 2 | H 3 | H 4 | V 5 | H 6 + | H 1 | V 2 | H 3 | V 4 | H 5 | H 6 + | V 1 | H 2 | H 3 | H 4 | V 5 | H 6 + | V 1 | H 2 | H 3 | V 4 | H 5 | H 6 ) .
| Ψ = α 2 | H a 1 | H V a 3 | V 2 | H 4 | H 5 + α β ( | H a 1 | H a 2 | H a 3 | H 2 | H 4 | V 5 + | H a 1 | H a 2 | H a 3 | H 2 | V 4 | H 5 + | V a 1 | V a 2 | V a 3 | V 2 | H 4 | H 5 + | V a 2 | H V a 3 | H 2 | H 4 | H 5 ) + β 2 ( | H V a 2 | H a 3 | V 2 | H 4 | V 5 + | H V a 2 | H a 3 | V 2 | V 4 | H 5 + | V a 1 | H V a 2 | H 2 | H 4 | V 5 + | V a 1 | H V a 2 | H 2 | V 4 | H 5 ) .
| Ψ = 1 2 2 { α β [ ( | H b 1 1 + | V b 1 2 ) ( | H b 2 1 + | V b 2 2 ) ( | H b 3 1 + | V b 3 2 ) | H 2 | H 4 | V 5 + ( | H b 1 1 + | V b 1 2 ) ( | H b 2 1 + | V b 2 2 ) ( | H b 3 1 + | V b 3 2 ) | H 2 | V 4 | H 5 + ( | H b 1 1 | V b 1 2 ) ( | H b 2 1 | V b 2 2 ) ( | H b 3 1 | V b 3 2 ) | V 2 | H 4 | H 5 ] + β 2 [ ( | 2 H b 2 1 | 2 V b 2 2 ) ( | H b 3 1 + | V b 3 2 ) | V 2 | H 4 | V 5 + ( | 2 H b 2 1 | 2 V b 2 2 ) ( | H b 3 1 + | V b 3 2 ) | V 2 | V 4 | H 5 + ( | H b 1 1 | V b 1 2 ) ( | 2 H b 2 1 | 2 V b 2 2 ) | H 2 | H 4 | V 5 + ( | H b 1 1 | V b 1 2 ) ( | 2 H b 2 1 | 2 V b 2 2 ) ( | H 2 | V 4 | H 5 ) ] + α 2 ( | H b 1 1 + | V b 1 2 ) ( | 2 H b 3 1 | 2 V b 3 2 ) | V 2 | H 4 | H 5 + α β ( | H b 2 1 | V b 2 2 ) ( | 2 H b 3 1 | 2 V b 3 2 ) | H 2 | H 4 | H 5 }
Π no = m = 0 ( 1 η ) m | m m | ,
Π click = 1 Π no = m = 1 [ 1 ( 1 η ) m ] | m m | .
ρ out = Tr b 1 1 , b 1 2 , b 2 1 , b 2 2 , b 3 1 , b 3 2 ( Π click b 1 1 Π click b 2 1 Π click b 3 1 Π no b 1 2 Π no b 2 2 Π no b 3 2 | Ψ Ψ | ) Tr b 1 1 , b 1 2 , b 2 1 , b 2 2 , b 3 1 , b 3 2 , 2 , 4 , 5 ( Π click b 1 1 Π click b 2 1 Π click b 3 1 Π no b 1 2 Π no b 2 2 Π no b 3 2 | Ψ Ψ | ) .
ρ out = | Φ out Φ out | ,
| Φ out = 1 3 ( | H 2 | H 4 | V 5 + | H 2 | V 4 | H 5 + | V 2 | H 4 | H 5 ) .
ρ out = | Φ out Φ out | ,
| Φ out = 1 3 ( | H 2 | H 4 | V 5 + | H 2 | V 4 | H 5 | V 2 | H 4 | H 5 ) ,
P t = P c P f ,
P f = 8 × Tr b 1 1 , b 1 2 , b 2 1 , b 2 2 , b 3 1 , b 3 2 , 2 , 4 , 5 ( Π click b 1 1 Π click b 2 1 Π click b 3 1 Π no b 1 2 Π no b 2 2 Π no b 3 2 | Ψ Ψ | ) = 3 | α β | 2 η 3 .
l c Δ L l p ,
α | H c in | H t in + β | H c in | V t in + γ | V c in | H t in + δ | V c in | V t in α | H S c out | H S t out + β | H S c out | V S t out + γ | V L c out | V L t out + δ | V L c out | H L t out ,
F = ψ W | ρ out | ψ W = 1 ,

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