Abstract

We propose a linear-optics-based scheme for local conversion of four Einstein-Podolsky-Rosen photon pairs distributed among five parties into four-photon polarization-entangled decoherence-free states using local operations and classical communication. The proposed setup involves simple linear optical elements and non-photon-number-resolving detectors that can only distinguish between the presence and absence of photons, and no information on the exact number of photons can be obtained. This greatly simplifies the experimental realization for linear optical quantum computation and quantum information processing.

© 2011 OSA

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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] [PubMed]
  2. L. K. Grover, “Quantum mechanics helps in searching for a needle in a haystack,” Phys. Rev. Lett. 79, 325 (1997).
    [CrossRef]
  3. H. F. Wang and S. Zhang, “Linear optical generation of multipartite entanglement with conventional photon detectors,” Phys. Rev. A 79, 042336 (2009).
    [CrossRef]
  4. C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in Proceedings of the IEEE International Conference on Computers, Systems and Signal Proceessing, Bangalore, India, (IEEE, New York, 1984), 175–179.
  5. M. Hillery, V. Buzek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
    [CrossRef]
  6. H. F. Wang, X. Ji, and S. Zhang, “Improving the security of multiparty quantum secret splitting and quantum state sharing,” Phys. Lett. A 358, 11–14 (2006).
    [CrossRef]
  7. C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69, 2881–2884 (1992).
    [CrossRef] [PubMed]
  8. C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett. 68, 3121–3124 (1992).
    [CrossRef] [PubMed]
  9. K. Boströem and T. Felbinger, “Deterministic secure direct communication using entanglement,” Phys. Rev. Lett. 89, 187902 (2002).
    [CrossRef]
  10. A. D. Zhu, Y. Xia, Q. B. Fan, and S. Zhang, “Secure direct communication based on secret transmitting order of particles,” Phys. Rev. A,  73, 022338 (2006).
    [CrossRef]
  11. D. A. Lidar, D. Bacon, and K. B. Whaley, “Concatenating decoherence-free subspaces with quantum error correcting codes,” Phys. Rev. Lett. 82, 4556–4559 (1999).
    [CrossRef]
  12. J. Kempe, D. Bacon, D. A. Lidar, and K. B. Whaley, “Theory of decoherence-free fault-tolerant universal quantum computation,” Phys. Rev. A 63, 042307 (2001).
    [CrossRef]
  13. M. Bourennane, M. Eibl, S. Gaertner, C. Kurtsiefer, A. Cabello, and H. Weinfurter, “Decoherence-free quantum information processing with four-photon entangled states,” Phys. Rev. Lett. 92, 107901 (2004).
    [CrossRef] [PubMed]
  14. X. B. Zou, J. Shu, and G. C. Guo, “Simple scheme for generating four-photon polarization-entangled decoherence-free states using spontaneous parametric down-conversions,” Phys. Rev. A 73, 054301 (2006)
    [CrossRef]
  15. Y. X. Gong, X. B. Zou, X. L. Niu, J. Li, Y. F. Huang, and G. C. Guo, “Generation of arbitrary four-photon polarization-entangled decoherence-free states,” Phys. Rev. A 77, 042317 (2008).
    [CrossRef]
  16. P. Kok and S. L. Braunstein, “Postselected versus nonpostselected quantum teleportation using parametric down-conversion,” Phys. Rev. A 61, 042304 (2000).
    [CrossRef]
  17. T. Yamamoto, K. Hayashi, S. K. Özdemir, M. Koashi, and N. Imoto, “Robust photonic entanglement distribution by state-independent encoding onto decoherence-free subspace,” Nat. Photon. 2, 488–491 (2008).
    [CrossRef]
  18. P. Walther, K. J. Resch, and A. Zeilinger, “Local conversion of Greenberger-Horne-Zeilinger states to approximate W states,” Phys. Rev. Lett. 94, 240501 (2005).
    [CrossRef]
  19. T. Tashima, T. Wakatsuki, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local transformation of two Einstein-Podolsky-Rosen photon pairs into a three-photon W state,” Phys. Rev. Lett. 102, 130502 (2009).
    [CrossRef] [PubMed]
  20. C. Y. Lu, X. Q. Zhou, O. Gühne, W. B. Gao, J. Zhang, Z. S. Yuan, A. Goebel, T. Yang, and J. W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
    [CrossRef]
  21. S. Glancy, J. M. LoSecco, H. M. Vasconcelos, and C. E. Tanner, “Imperfect detectors in linear optical quantum computers,” Phys. Rev. A 65, 062317 (2002).
    [CrossRef]

2009 (2)

H. F. Wang and S. Zhang, “Linear optical generation of multipartite entanglement with conventional photon detectors,” Phys. Rev. A 79, 042336 (2009).
[CrossRef]

T. Tashima, T. Wakatsuki, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local transformation of two Einstein-Podolsky-Rosen photon pairs into a three-photon W state,” Phys. Rev. Lett. 102, 130502 (2009).
[CrossRef] [PubMed]

2008 (2)

Y. X. Gong, X. B. Zou, X. L. Niu, J. Li, Y. F. Huang, and G. C. Guo, “Generation of arbitrary four-photon polarization-entangled decoherence-free states,” Phys. Rev. A 77, 042317 (2008).
[CrossRef]

T. Yamamoto, K. Hayashi, S. K. Özdemir, M. Koashi, and N. Imoto, “Robust photonic entanglement distribution by state-independent encoding onto decoherence-free subspace,” Nat. Photon. 2, 488–491 (2008).
[CrossRef]

2007 (1)

C. Y. Lu, X. Q. Zhou, O. Gühne, W. B. Gao, J. Zhang, Z. S. Yuan, A. Goebel, T. Yang, and J. W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
[CrossRef]

2006 (3)

X. B. Zou, J. Shu, and G. C. Guo, “Simple scheme for generating four-photon polarization-entangled decoherence-free states using spontaneous parametric down-conversions,” Phys. Rev. A 73, 054301 (2006)
[CrossRef]

H. F. Wang, X. Ji, and S. Zhang, “Improving the security of multiparty quantum secret splitting and quantum state sharing,” Phys. Lett. A 358, 11–14 (2006).
[CrossRef]

A. D. Zhu, Y. Xia, Q. B. Fan, and S. Zhang, “Secure direct communication based on secret transmitting order of particles,” Phys. Rev. A,  73, 022338 (2006).
[CrossRef]

2005 (1)

P. Walther, K. J. Resch, and A. Zeilinger, “Local conversion of Greenberger-Horne-Zeilinger states to approximate W states,” Phys. Rev. Lett. 94, 240501 (2005).
[CrossRef]

2004 (1)

M. Bourennane, M. Eibl, S. Gaertner, C. Kurtsiefer, A. Cabello, and H. Weinfurter, “Decoherence-free quantum information processing with four-photon entangled states,” Phys. Rev. Lett. 92, 107901 (2004).
[CrossRef] [PubMed]

2002 (2)

K. Boströem and T. Felbinger, “Deterministic secure direct communication using entanglement,” Phys. Rev. Lett. 89, 187902 (2002).
[CrossRef]

S. Glancy, J. M. LoSecco, H. M. Vasconcelos, and C. E. Tanner, “Imperfect detectors in linear optical quantum computers,” Phys. Rev. A 65, 062317 (2002).
[CrossRef]

2001 (1)

J. Kempe, D. Bacon, D. A. Lidar, and K. B. Whaley, “Theory of decoherence-free fault-tolerant universal quantum computation,” Phys. Rev. A 63, 042307 (2001).
[CrossRef]

2000 (1)

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

1999 (2)

D. A. Lidar, D. Bacon, and K. B. Whaley, “Concatenating decoherence-free subspaces with quantum error correcting codes,” Phys. Rev. Lett. 82, 4556–4559 (1999).
[CrossRef]

M. Hillery, V. Buzek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
[CrossRef]

1997 (1)

L. K. Grover, “Quantum mechanics helps in searching for a needle in a haystack,” Phys. Rev. Lett. 79, 325 (1997).
[CrossRef]

1993 (1)

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef] [PubMed]

1992 (2)

C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69, 2881–2884 (1992).
[CrossRef] [PubMed]

C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett. 68, 3121–3124 (1992).
[CrossRef] [PubMed]

Bacon, D.

J. Kempe, D. Bacon, D. A. Lidar, and K. B. Whaley, “Theory of decoherence-free fault-tolerant universal quantum computation,” Phys. Rev. A 63, 042307 (2001).
[CrossRef]

D. A. Lidar, D. Bacon, and K. B. Whaley, “Concatenating decoherence-free subspaces with quantum error correcting codes,” Phys. Rev. Lett. 82, 4556–4559 (1999).
[CrossRef]

Bennett, C. H.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef] [PubMed]

C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett. 68, 3121–3124 (1992).
[CrossRef] [PubMed]

C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69, 2881–2884 (1992).
[CrossRef] [PubMed]

C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in Proceedings of the IEEE International Conference on Computers, Systems and Signal Proceessing, Bangalore, India, (IEEE, New York, 1984), 175–179.

Berthiaume, A.

M. Hillery, V. Buzek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
[CrossRef]

Boströem, K.

K. Boströem and T. Felbinger, “Deterministic secure direct communication using entanglement,” Phys. Rev. Lett. 89, 187902 (2002).
[CrossRef]

Bourennane, M.

M. Bourennane, M. Eibl, S. Gaertner, C. Kurtsiefer, A. Cabello, and H. Weinfurter, “Decoherence-free quantum information processing with four-photon entangled states,” Phys. Rev. Lett. 92, 107901 (2004).
[CrossRef] [PubMed]

Brassard, G.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef] [PubMed]

C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” in Proceedings of the IEEE International Conference on Computers, Systems and Signal Proceessing, Bangalore, India, (IEEE, New York, 1984), 175–179.

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]

Buzek, V.

M. Hillery, V. Buzek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
[CrossRef]

Cabello, A.

M. Bourennane, M. Eibl, S. Gaertner, C. Kurtsiefer, A. Cabello, and H. Weinfurter, “Decoherence-free quantum information processing with four-photon entangled states,” Phys. Rev. Lett. 92, 107901 (2004).
[CrossRef] [PubMed]

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] [PubMed]

Eibl, M.

M. Bourennane, M. Eibl, S. Gaertner, C. Kurtsiefer, A. Cabello, and H. Weinfurter, “Decoherence-free quantum information processing with four-photon entangled states,” Phys. Rev. Lett. 92, 107901 (2004).
[CrossRef] [PubMed]

Fan, Q. B.

A. D. Zhu, Y. Xia, Q. B. Fan, and S. Zhang, “Secure direct communication based on secret transmitting order of particles,” Phys. Rev. A,  73, 022338 (2006).
[CrossRef]

Felbinger, T.

K. Boströem and T. Felbinger, “Deterministic secure direct communication using entanglement,” Phys. Rev. Lett. 89, 187902 (2002).
[CrossRef]

Gaertner, S.

M. Bourennane, M. Eibl, S. Gaertner, C. Kurtsiefer, A. Cabello, and H. Weinfurter, “Decoherence-free quantum information processing with four-photon entangled states,” Phys. Rev. Lett. 92, 107901 (2004).
[CrossRef] [PubMed]

Gao, W. B.

C. Y. Lu, X. Q. Zhou, O. Gühne, W. B. Gao, J. Zhang, Z. S. Yuan, A. Goebel, T. Yang, and J. W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
[CrossRef]

Glancy, S.

S. Glancy, J. M. LoSecco, H. M. Vasconcelos, and C. E. Tanner, “Imperfect detectors in linear optical quantum computers,” Phys. Rev. A 65, 062317 (2002).
[CrossRef]

Goebel, A.

C. Y. Lu, X. Q. Zhou, O. Gühne, W. B. Gao, J. Zhang, Z. S. Yuan, A. Goebel, T. Yang, and J. W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
[CrossRef]

Gong, Y. X.

Y. X. Gong, X. B. Zou, X. L. Niu, J. Li, Y. F. Huang, and G. C. Guo, “Generation of arbitrary four-photon polarization-entangled decoherence-free states,” Phys. Rev. A 77, 042317 (2008).
[CrossRef]

Grover, L. K.

L. K. Grover, “Quantum mechanics helps in searching for a needle in a haystack,” Phys. Rev. Lett. 79, 325 (1997).
[CrossRef]

Gühne, O.

C. Y. Lu, X. Q. Zhou, O. Gühne, W. B. Gao, J. Zhang, Z. S. Yuan, A. Goebel, T. Yang, and J. W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
[CrossRef]

Guo, G. C.

Y. X. Gong, X. B. Zou, X. L. Niu, J. Li, Y. F. Huang, and G. C. Guo, “Generation of arbitrary four-photon polarization-entangled decoherence-free states,” Phys. Rev. A 77, 042317 (2008).
[CrossRef]

X. B. Zou, J. Shu, and G. C. Guo, “Simple scheme for generating four-photon polarization-entangled decoherence-free states using spontaneous parametric down-conversions,” Phys. Rev. A 73, 054301 (2006)
[CrossRef]

Hayashi, K.

T. Yamamoto, K. Hayashi, S. K. Özdemir, M. Koashi, and N. Imoto, “Robust photonic entanglement distribution by state-independent encoding onto decoherence-free subspace,” Nat. Photon. 2, 488–491 (2008).
[CrossRef]

Hillery, M.

M. Hillery, V. Buzek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A 59, 1829–1834 (1999).
[CrossRef]

Huang, Y. F.

Y. X. Gong, X. B. Zou, X. L. Niu, J. Li, Y. F. Huang, and G. C. Guo, “Generation of arbitrary four-photon polarization-entangled decoherence-free states,” Phys. Rev. A 77, 042317 (2008).
[CrossRef]

Imoto, N.

T. Tashima, T. Wakatsuki, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local transformation of two Einstein-Podolsky-Rosen photon pairs into a three-photon W state,” Phys. Rev. Lett. 102, 130502 (2009).
[CrossRef] [PubMed]

T. Yamamoto, K. Hayashi, S. K. Özdemir, M. Koashi, and N. Imoto, “Robust photonic entanglement distribution by state-independent encoding onto decoherence-free subspace,” Nat. Photon. 2, 488–491 (2008).
[CrossRef]

Ji, X.

H. F. Wang, X. Ji, and S. Zhang, “Improving the security of multiparty quantum secret splitting and quantum state sharing,” Phys. Lett. A 358, 11–14 (2006).
[CrossRef]

Jozsa, R.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef] [PubMed]

Kempe, J.

J. Kempe, D. Bacon, D. A. Lidar, and K. B. Whaley, “Theory of decoherence-free fault-tolerant universal quantum computation,” Phys. Rev. A 63, 042307 (2001).
[CrossRef]

Koashi, M.

T. Tashima, T. Wakatsuki, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local transformation of two Einstein-Podolsky-Rosen photon pairs into a three-photon W state,” Phys. Rev. Lett. 102, 130502 (2009).
[CrossRef] [PubMed]

T. Yamamoto, K. Hayashi, S. K. Özdemir, M. Koashi, and N. Imoto, “Robust photonic entanglement distribution by state-independent encoding onto decoherence-free subspace,” Nat. Photon. 2, 488–491 (2008).
[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]

Kurtsiefer, C.

M. Bourennane, M. Eibl, S. Gaertner, C. Kurtsiefer, A. Cabello, and H. Weinfurter, “Decoherence-free quantum information processing with four-photon entangled states,” Phys. Rev. Lett. 92, 107901 (2004).
[CrossRef] [PubMed]

Li, J.

Y. X. Gong, X. B. Zou, X. L. Niu, J. Li, Y. F. Huang, and G. C. Guo, “Generation of arbitrary four-photon polarization-entangled decoherence-free states,” Phys. Rev. A 77, 042317 (2008).
[CrossRef]

Lidar, D. A.

J. Kempe, D. Bacon, D. A. Lidar, and K. B. Whaley, “Theory of decoherence-free fault-tolerant universal quantum computation,” Phys. Rev. A 63, 042307 (2001).
[CrossRef]

D. A. Lidar, D. Bacon, and K. B. Whaley, “Concatenating decoherence-free subspaces with quantum error correcting codes,” Phys. Rev. Lett. 82, 4556–4559 (1999).
[CrossRef]

LoSecco, J. M.

S. Glancy, J. M. LoSecco, H. M. Vasconcelos, and C. E. Tanner, “Imperfect detectors in linear optical quantum computers,” Phys. Rev. A 65, 062317 (2002).
[CrossRef]

Lu, C. Y.

C. Y. Lu, X. Q. Zhou, O. Gühne, W. B. Gao, J. Zhang, Z. S. Yuan, A. Goebel, T. Yang, and J. W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
[CrossRef]

Niu, X. L.

Y. X. Gong, X. B. Zou, X. L. Niu, J. Li, Y. F. Huang, and G. C. Guo, “Generation of arbitrary four-photon polarization-entangled decoherence-free states,” Phys. Rev. A 77, 042317 (2008).
[CrossRef]

Özdemir, S. K.

T. Tashima, T. Wakatsuki, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local transformation of two Einstein-Podolsky-Rosen photon pairs into a three-photon W state,” Phys. Rev. Lett. 102, 130502 (2009).
[CrossRef] [PubMed]

T. Yamamoto, K. Hayashi, S. K. Özdemir, M. Koashi, and N. Imoto, “Robust photonic entanglement distribution by state-independent encoding onto decoherence-free subspace,” Nat. Photon. 2, 488–491 (2008).
[CrossRef]

Pan, J. W.

C. Y. Lu, X. Q. Zhou, O. Gühne, W. B. Gao, J. Zhang, Z. S. Yuan, A. Goebel, T. Yang, and J. W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
[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] [PubMed]

Resch, K. J.

P. Walther, K. J. Resch, and A. Zeilinger, “Local conversion of Greenberger-Horne-Zeilinger states to approximate W states,” Phys. Rev. Lett. 94, 240501 (2005).
[CrossRef]

Shu, J.

X. B. Zou, J. Shu, and G. C. Guo, “Simple scheme for generating four-photon polarization-entangled decoherence-free states using spontaneous parametric down-conversions,” Phys. Rev. A 73, 054301 (2006)
[CrossRef]

Tanner, C. E.

S. Glancy, J. M. LoSecco, H. M. Vasconcelos, and C. E. Tanner, “Imperfect detectors in linear optical quantum computers,” Phys. Rev. A 65, 062317 (2002).
[CrossRef]

Tashima, T.

T. Tashima, T. Wakatsuki, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local transformation of two Einstein-Podolsky-Rosen photon pairs into a three-photon W state,” Phys. Rev. Lett. 102, 130502 (2009).
[CrossRef] [PubMed]

Vasconcelos, H. M.

S. Glancy, J. M. LoSecco, H. M. Vasconcelos, and C. E. Tanner, “Imperfect detectors in linear optical quantum computers,” Phys. Rev. A 65, 062317 (2002).
[CrossRef]

Wakatsuki, T.

T. Tashima, T. Wakatsuki, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local transformation of two Einstein-Podolsky-Rosen photon pairs into a three-photon W state,” Phys. Rev. Lett. 102, 130502 (2009).
[CrossRef] [PubMed]

Walther, P.

P. Walther, K. J. Resch, and A. Zeilinger, “Local conversion of Greenberger-Horne-Zeilinger states to approximate W states,” Phys. Rev. Lett. 94, 240501 (2005).
[CrossRef]

Wang, H. F.

H. F. Wang and S. Zhang, “Linear optical generation of multipartite entanglement with conventional photon detectors,” Phys. Rev. A 79, 042336 (2009).
[CrossRef]

H. F. Wang, X. Ji, and S. Zhang, “Improving the security of multiparty quantum secret splitting and quantum state sharing,” Phys. Lett. A 358, 11–14 (2006).
[CrossRef]

Weinfurter, H.

M. Bourennane, M. Eibl, S. Gaertner, C. Kurtsiefer, A. Cabello, and H. Weinfurter, “Decoherence-free quantum information processing with four-photon entangled states,” Phys. Rev. Lett. 92, 107901 (2004).
[CrossRef] [PubMed]

Whaley, K. B.

J. Kempe, D. Bacon, D. A. Lidar, and K. B. Whaley, “Theory of decoherence-free fault-tolerant universal quantum computation,” Phys. Rev. A 63, 042307 (2001).
[CrossRef]

D. A. Lidar, D. Bacon, and K. B. Whaley, “Concatenating decoherence-free subspaces with quantum error correcting codes,” Phys. Rev. Lett. 82, 4556–4559 (1999).
[CrossRef]

Wiesner, S. J.

C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. 69, 2881–2884 (1992).
[CrossRef] [PubMed]

Wootters, W. K.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
[CrossRef] [PubMed]

Xia, Y.

A. D. Zhu, Y. Xia, Q. B. Fan, and S. Zhang, “Secure direct communication based on secret transmitting order of particles,” Phys. Rev. A,  73, 022338 (2006).
[CrossRef]

Yamamoto, T.

T. Tashima, T. Wakatsuki, Ş. K. Özdemir, T. Yamamoto, M. Koashi, and N. Imoto, “Local transformation of two Einstein-Podolsky-Rosen photon pairs into a three-photon W state,” Phys. Rev. Lett. 102, 130502 (2009).
[CrossRef] [PubMed]

T. Yamamoto, K. Hayashi, S. K. Özdemir, M. Koashi, and N. Imoto, “Robust photonic entanglement distribution by state-independent encoding onto decoherence-free subspace,” Nat. Photon. 2, 488–491 (2008).
[CrossRef]

Yang, T.

C. Y. Lu, X. Q. Zhou, O. Gühne, W. B. Gao, J. Zhang, Z. S. Yuan, A. Goebel, T. Yang, and J. W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
[CrossRef]

Yuan, Z. S.

C. Y. Lu, X. Q. Zhou, O. Gühne, W. B. Gao, J. Zhang, Z. S. Yuan, A. Goebel, T. Yang, and J. W. Pan, “Experimental entanglement of six photons in graph states,” Nat. Phys. 3, 91–95 (2007).
[CrossRef]

Zeilinger, A.

P. Walther, K. J. Resch, and A. Zeilinger, “Local conversion of Greenberger-Horne-Zeilinger states to approximate W states,” Phys. Rev. Lett. 94, 240501 (2005).
[CrossRef]

Zhang, J.

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