Abstract

We propose a protocol for the controlled generation of four-photon polarization-entangled decoherence-free states with a certain success probability. The proposed setup involves simple linear optical elements, two single-photon polarzaition entangled states, a pair of two-photon polarization entangled states, and conventional photon detectors that only distinguish the vacuum and nonvacuum Fock number states. This makes the protocol more realizable in experiments.

© 2008 Optical Society of America

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  1. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145-195 (2002).
    [CrossRef]
  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]
  3. 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]
  4. F. G. Deng and G. L. Long, “Controlled order rearrangement encryption for quantum key distribution,” Phys. Rev. A 68, 042315 (2003).
    [CrossRef]
  5. X. B. Wang, “Quantum key distribution with two-qubit quantum codes,” Phys. Rev. Lett. 92, 077902 (2004).
    [CrossRef] [PubMed]
  6. C. H. Bennett, D. P. DiCincenzo, P. W. Shor, J. A. Smolin, B. M. Terhal, and W. K. Wotters, “Remote state preparation,” Phys. Rev. Lett. 87, 077902 (2001).
    [CrossRef] [PubMed]
  7. P. W. Shor, “Scheme for reducing decoherence in quantum computer memory,” Phys. Rev. A 52, R2493-R2496 (1995).
    [CrossRef] [PubMed]
  8. A. M. Steane, “Error correcting codes in quantum theory,” Phys. Rev. Lett. 77, 793-797 (1996).
    [CrossRef] [PubMed]
  9. R. Laflamme, C. Miquel, J. P. Paz, and W. H. Zurek, “Perfect quantum error correcting code,” Phys. Rev. Lett. 77, 198-201 (1996).
    [CrossRef] [PubMed]
  10. L. Viola, E. Knill, and S. Lloyd, “Dynamical decoupling of open quantum systems,” Phys. Rev. Lett. 82, 2417-2421 (1999).
    [CrossRef]
  11. 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]
  12. S. D. Bartlett, T. Rudolph, and R. W. Spekkens, “Classical and quantum communication without a shared reference frame,” Phys. Rev. Lett. 91, 027901 (2003).
    [CrossRef] [PubMed]
  13. J. C. Boileau, D. Gottesman, R. Laflamme, D. Poulin, and R. W. Spekkens, “Robust polarization-based quantum key distribution over a collective-noise channel,” Phys. Rev. Lett. 92, 017901 (2004).
    [CrossRef] [PubMed]
  14. A. Cabello, “Greenberger-Horne-Zeilinger-like proof of Bells theorem involving observers who do not share a reference frame,” Phys. Rev. A 68, 042104 (2003).
    [CrossRef]
  15. A. Cabello, “Bells theorem without inequalities and without alignments,” Phys. Rev. Lett. 91, 230403 (2004).
    [CrossRef]
  16. G. M. Palma, K. A. Suominen, and A. K. Ekert, “Quantum computers and dissipation,” arXiv:quant-ph/9702001v/.
  17. L. M. Duan and G. C. Guo, “Preserving coherence in quantum computation by pairing quantum bits,” Phys. Rev. Lett. 79, 1953-1956 (1997).
    [CrossRef]
  18. P. Zanardi and M. Rasetti, “Noiseless quantum codes,” Phys. Rev. Lett. 79, 3306-3309 (1997).
    [CrossRef]
  19. J. B. Altepeter, P. G. Hadley, S. M. Wendelken, A. J. Berglund, and P. G. Kwiat, “Experimental investigation of a two-qubit decoherence-free subspace,” Phys. Rev. Lett. 92, 147901 (2004).
    [CrossRef] [PubMed]
  20. 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]
  21. 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]
  22. 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]
  23. 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]
  24. T. B. Pittman, B. C. Jacobs, J. D. Franson, “Probabilistic quantum encoder for single-photon qubits,” Phys. Rev. A 69, 042306 (2004).
    [CrossRef]
  25. X. B. Zou, S. L. Zhang, K. L. 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]
  26. 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]
  27. W. T. Liu, W. Wu, B. Q. Ou, P. X. Chen, C. Z. Li, and J. M. Yuan, “Experimental remote preparation of arbitrary photon polarization states,” Phys. Rev. A 76, 022308 (2007).
    [CrossRef]
  28. Y. Xia, J. Song, and H. S. Song, “Linear optical protocol for preparation of N-photon Greenberger-Horne-Zeilinger state with conventional photon detectors,” Appl. Phys. Lett. 92, 021128 (2008).
    [CrossRef]
  29. M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
    [CrossRef] [PubMed]
  30. J. W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature (London) 403, 515-519 (2000).
    [CrossRef]
  31. D. Bouwmeester, J. W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345-1349 (1999).
    [CrossRef]
  32. J. W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435-4438 (2001).
    [CrossRef] [PubMed]
  33. O. Benson, C. Santori, M. Pelton, and Y. Yanmamoto, “Regulated and entangled photons from a single quantum dot,” Phys. Rev. Lett. 84, 2513-2516 (2000).
    [CrossRef] [PubMed]
  34. 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]

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]

Y. Xia, J. Song, and H. S. Song, “Linear optical protocol for preparation of N-photon Greenberger-Horne-Zeilinger state with conventional photon detectors,” Appl. Phys. Lett. 92, 021128 (2008).
[CrossRef]

2007 (2)

X. B. Zou, S. L. Zhang, K. L. 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]

W. T. Liu, W. Wu, B. Q. Ou, P. X. Chen, C. Z. Li, and J. M. Yuan, “Experimental remote preparation of arbitrary photon polarization states,” Phys. Rev. A 76, 022308 (2007).
[CrossRef]

2006 (3)

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]

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, 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]

2004 (7)

T. B. Pittman, B. C. Jacobs, J. D. Franson, “Probabilistic quantum encoder for single-photon qubits,” Phys. Rev. A 69, 042306 (2004).
[CrossRef]

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
[CrossRef] [PubMed]

X. B. Wang, “Quantum key distribution with two-qubit quantum codes,” Phys. Rev. Lett. 92, 077902 (2004).
[CrossRef] [PubMed]

J. C. Boileau, D. Gottesman, R. Laflamme, D. Poulin, and R. W. Spekkens, “Robust polarization-based quantum key distribution over a collective-noise channel,” Phys. Rev. Lett. 92, 017901 (2004).
[CrossRef] [PubMed]

A. Cabello, “Bells theorem without inequalities and without alignments,” Phys. Rev. Lett. 91, 230403 (2004).
[CrossRef]

J. B. Altepeter, P. G. Hadley, S. M. Wendelken, A. J. Berglund, and P. G. Kwiat, “Experimental investigation of a two-qubit decoherence-free subspace,” Phys. Rev. Lett. 92, 147901 (2004).
[CrossRef] [PubMed]

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]

2003 (3)

A. Cabello, “Greenberger-Horne-Zeilinger-like proof of Bells theorem involving observers who do not share a reference frame,” Phys. Rev. A 68, 042104 (2003).
[CrossRef]

S. D. Bartlett, T. Rudolph, and R. W. Spekkens, “Classical and quantum communication without a shared reference frame,” Phys. Rev. Lett. 91, 027901 (2003).
[CrossRef] [PubMed]

F. G. Deng and G. L. Long, “Controlled order rearrangement encryption for quantum key distribution,” Phys. Rev. A 68, 042315 (2003).
[CrossRef]

2002 (1)

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

2001 (4)

C. H. Bennett, D. P. DiCincenzo, P. W. Shor, J. A. Smolin, B. M. Terhal, and W. K. Wotters, “Remote state preparation,” Phys. Rev. Lett. 87, 077902 (2001).
[CrossRef] [PubMed]

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]

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, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435-4438 (2001).
[CrossRef] [PubMed]

2000 (2)

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

J. W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature (London) 403, 515-519 (2000).
[CrossRef]

1999 (2)

D. Bouwmeester, J. W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345-1349 (1999).
[CrossRef]

L. Viola, E. Knill, and S. Lloyd, “Dynamical decoupling of open quantum systems,” Phys. Rev. Lett. 82, 2417-2421 (1999).
[CrossRef]

1997 (2)

L. M. Duan and G. C. Guo, “Preserving coherence in quantum computation by pairing quantum bits,” Phys. Rev. Lett. 79, 1953-1956 (1997).
[CrossRef]

P. Zanardi and M. Rasetti, “Noiseless quantum codes,” Phys. Rev. Lett. 79, 3306-3309 (1997).
[CrossRef]

1996 (2)

A. M. Steane, “Error correcting codes in quantum theory,” Phys. Rev. Lett. 77, 793-797 (1996).
[CrossRef] [PubMed]

R. Laflamme, C. Miquel, J. P. Paz, and W. H. Zurek, “Perfect quantum error correcting code,” Phys. Rev. Lett. 77, 198-201 (1996).
[CrossRef] [PubMed]

1995 (1)

P. W. Shor, “Scheme for reducing decoherence in quantum computer memory,” Phys. Rev. A 52, R2493-R2496 (1995).
[CrossRef] [PubMed]

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] [PubMed]

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] [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]

Altepeter, J. B.

J. B. Altepeter, P. G. Hadley, S. M. Wendelken, A. J. Berglund, and P. G. Kwiat, “Experimental investigation of a two-qubit decoherence-free subspace,” Phys. Rev. Lett. 92, 147901 (2004).
[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]

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]

Bartlett, S. D.

S. D. Bartlett, T. Rudolph, and R. W. Spekkens, “Classical and quantum communication without a shared reference frame,” Phys. Rev. Lett. 91, 027901 (2003).
[CrossRef] [PubMed]

Bennett, C. H.

C. H. Bennett, D. P. DiCincenzo, P. W. Shor, J. A. Smolin, B. M. Terhal, and W. K. Wotters, “Remote state preparation,” Phys. Rev. Lett. 87, 077902 (2001).
[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]

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]

Benson, O.

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

Berglund, A. J.

J. B. Altepeter, P. G. Hadley, S. M. Wendelken, A. J. Berglund, and P. G. Kwiat, “Experimental investigation of a two-qubit decoherence-free subspace,” Phys. Rev. Lett. 92, 147901 (2004).
[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]

Boileau, J. C.

J. C. Boileau, D. Gottesman, R. Laflamme, D. Poulin, and R. W. Spekkens, “Robust polarization-based quantum key distribution over a collective-noise channel,” Phys. Rev. Lett. 92, 017901 (2004).
[CrossRef] [PubMed]

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]

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
[CrossRef] [PubMed]

Bouwmeester, D.

J. W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature (London) 403, 515-519 (2000).
[CrossRef]

D. Bouwmeester, J. W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345-1349 (1999).
[CrossRef]

Brassard, G.

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]

Cabello, A.

A. Cabello, “Bells theorem without inequalities and without alignments,” Phys. Rev. Lett. 91, 230403 (2004).
[CrossRef]

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]

A. Cabello, “Greenberger-Horne-Zeilinger-like proof of Bells theorem involving observers who do not share a reference frame,” Phys. Rev. A 68, 042104 (2003).
[CrossRef]

Chen, P. X.

W. T. Liu, W. Wu, B. Q. Ou, P. X. Chen, C. Z. Li, and J. M. Yuan, “Experimental remote preparation of arbitrary photon polarization states,” Phys. Rev. A 76, 022308 (2007).
[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]

Daniell, M.

J. W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435-4438 (2001).
[CrossRef] [PubMed]

J. W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature (London) 403, 515-519 (2000).
[CrossRef]

D. Bouwmeester, J. W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345-1349 (1999).
[CrossRef]

Deng, F. G.

F. G. Deng and G. L. Long, “Controlled order rearrangement encryption for quantum key distribution,” Phys. Rev. A 68, 042315 (2003).
[CrossRef]

DiCincenzo, D. P.

C. H. Bennett, D. P. DiCincenzo, P. W. Shor, J. A. Smolin, B. M. Terhal, and W. K. Wotters, “Remote state preparation,” Phys. Rev. Lett. 87, 077902 (2001).
[CrossRef] [PubMed]

Duan, L. M.

L. M. Duan and G. C. Guo, “Preserving coherence in quantum computation by pairing quantum bits,” Phys. Rev. Lett. 79, 1953-1956 (1997).
[CrossRef]

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]

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
[CrossRef] [PubMed]

Ekert, A. K.

G. M. Palma, K. A. Suominen, and A. K. Ekert, “Quantum computers and dissipation,” arXiv:quant-ph/9702001v/.

Franson, J. D.

T. B. Pittman, B. C. Jacobs, J. D. Franson, “Probabilistic quantum encoder for single-photon qubits,” Phys. Rev. A 69, 042306 (2004).
[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]

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]

Gasparoni, S.

J. W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435-4438 (2001).
[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]

Gisin, N.

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

Gottesman, D.

J. C. Boileau, D. Gottesman, R. Laflamme, D. Poulin, and R. W. Spekkens, “Robust polarization-based quantum key distribution over a collective-noise channel,” Phys. Rev. Lett. 92, 017901 (2004).
[CrossRef] [PubMed]

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, S. L. Zhang, K. L. 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, 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]

L. M. Duan and G. C. Guo, “Preserving coherence in quantum computation by pairing quantum bits,” Phys. Rev. Lett. 79, 1953-1956 (1997).
[CrossRef]

Hadley, P. G.

J. B. Altepeter, P. G. Hadley, S. M. Wendelken, A. J. Berglund, and P. G. Kwiat, “Experimental investigation of a two-qubit decoherence-free subspace,” Phys. Rev. Lett. 92, 147901 (2004).
[CrossRef] [PubMed]

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]

Jacobs, B. C.

T. B. Pittman, B. C. Jacobs, J. D. Franson, “Probabilistic quantum encoder for single-photon qubits,” Phys. Rev. A 69, 042306 (2004).
[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]

Jozsa, R.

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]

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]

Kiesel, N.

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
[CrossRef] [PubMed]

Knill, E.

L. Viola, E. Knill, and S. Lloyd, “Dynamical decoupling of open quantum systems,” Phys. Rev. Lett. 82, 2417-2421 (1999).
[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]

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
[CrossRef] [PubMed]

Kwiat, P. G.

J. B. Altepeter, P. G. Hadley, S. M. Wendelken, A. J. Berglund, and P. G. Kwiat, “Experimental investigation of a two-qubit decoherence-free subspace,” Phys. Rev. Lett. 92, 147901 (2004).
[CrossRef] [PubMed]

Laflamme, R.

J. C. Boileau, D. Gottesman, R. Laflamme, D. Poulin, and R. W. Spekkens, “Robust polarization-based quantum key distribution over a collective-noise channel,” Phys. Rev. Lett. 92, 017901 (2004).
[CrossRef] [PubMed]

R. Laflamme, C. Miquel, J. P. Paz, and W. H. Zurek, “Perfect quantum error correcting code,” Phys. Rev. Lett. 77, 198-201 (1996).
[CrossRef] [PubMed]

Li, C. Z.

W. T. Liu, W. Wu, B. Q. Ou, P. X. Chen, C. Z. Li, and J. M. Yuan, “Experimental remote preparation of arbitrary photon polarization states,” Phys. Rev. A 76, 022308 (2007).
[CrossRef]

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]

Li, K.

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]

Li, K. L.

X. B. Zou, S. L. Zhang, K. L. 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]

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]

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]

Liu, W. T.

W. T. Liu, W. Wu, B. Q. Ou, P. X. Chen, C. Z. Li, and J. M. Yuan, “Experimental remote preparation of arbitrary photon polarization states,” Phys. Rev. A 76, 022308 (2007).
[CrossRef]

Lloyd, S.

L. Viola, E. Knill, and S. Lloyd, “Dynamical decoupling of open quantum systems,” Phys. Rev. Lett. 82, 2417-2421 (1999).
[CrossRef]

Long, G. L.

F. G. Deng and G. L. Long, “Controlled order rearrangement encryption for quantum key distribution,” Phys. Rev. A 68, 042315 (2003).
[CrossRef]

Miquel, C.

R. Laflamme, C. Miquel, J. P. Paz, and W. H. Zurek, “Perfect quantum error correcting code,” Phys. Rev. Lett. 77, 198-201 (1996).
[CrossRef] [PubMed]

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]

Ou, B. Q.

W. T. Liu, W. Wu, B. Q. Ou, P. X. Chen, C. Z. Li, and J. M. Yuan, “Experimental remote preparation of arbitrary photon polarization states,” Phys. Rev. A 76, 022308 (2007).
[CrossRef]

Palma, G. M.

G. M. Palma, K. A. Suominen, and A. K. Ekert, “Quantum computers and dissipation,” arXiv:quant-ph/9702001v/.

Pan, J. W.

J. W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435-4438 (2001).
[CrossRef] [PubMed]

J. W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature (London) 403, 515-519 (2000).
[CrossRef]

D. Bouwmeester, J. W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345-1349 (1999).
[CrossRef]

Paz, J. P.

R. Laflamme, C. Miquel, J. P. Paz, and W. H. Zurek, “Perfect quantum error correcting code,” Phys. Rev. Lett. 77, 198-201 (1996).
[CrossRef] [PubMed]

Pelton, M.

O. Benson, C. Santori, M. Pelton, and Y. Yanmamoto, “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, J. D. Franson, “Probabilistic quantum encoder for single-photon qubits,” Phys. Rev. A 69, 042306 (2004).
[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]

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]

Poulin, D.

J. C. Boileau, D. Gottesman, R. Laflamme, D. Poulin, and R. W. Spekkens, “Robust polarization-based quantum key distribution over a collective-noise channel,” Phys. Rev. Lett. 92, 017901 (2004).
[CrossRef] [PubMed]

Rasetti, M.

P. Zanardi and M. Rasetti, “Noiseless quantum codes,” Phys. Rev. Lett. 79, 3306-3309 (1997).
[CrossRef]

Ribordy, G.

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

Rudolph, T.

S. D. Bartlett, T. Rudolph, and R. W. Spekkens, “Classical and quantum communication without a shared reference frame,” Phys. Rev. Lett. 91, 027901 (2003).
[CrossRef] [PubMed]

Santori, C.

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

Shor, P. W.

C. H. Bennett, D. P. DiCincenzo, P. W. Shor, J. A. Smolin, B. M. Terhal, and W. K. Wotters, “Remote state preparation,” Phys. Rev. Lett. 87, 077902 (2001).
[CrossRef] [PubMed]

P. W. Shor, “Scheme for reducing decoherence in quantum computer memory,” Phys. Rev. A 52, R2493-R2496 (1995).
[CrossRef] [PubMed]

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]

Smolin, J. A.

C. H. Bennett, D. P. DiCincenzo, P. W. Shor, J. A. Smolin, B. M. Terhal, and W. K. Wotters, “Remote state preparation,” Phys. Rev. Lett. 87, 077902 (2001).
[CrossRef] [PubMed]

Song, H. S.

Y. Xia, J. Song, and H. S. Song, “Linear optical protocol for preparation of N-photon Greenberger-Horne-Zeilinger state with conventional photon detectors,” Appl. Phys. Lett. 92, 021128 (2008).
[CrossRef]

Song, J.

Y. Xia, J. Song, and H. S. Song, “Linear optical protocol for preparation of N-photon Greenberger-Horne-Zeilinger state with conventional photon detectors,” Appl. Phys. Lett. 92, 021128 (2008).
[CrossRef]

Spekkens, R. W.

J. C. Boileau, D. Gottesman, R. Laflamme, D. Poulin, and R. W. Spekkens, “Robust polarization-based quantum key distribution over a collective-noise channel,” Phys. Rev. Lett. 92, 017901 (2004).
[CrossRef] [PubMed]

S. D. Bartlett, T. Rudolph, and R. W. Spekkens, “Classical and quantum communication without a shared reference frame,” Phys. Rev. Lett. 91, 027901 (2003).
[CrossRef] [PubMed]

Steane, A. M.

A. M. Steane, “Error correcting codes in quantum theory,” Phys. Rev. Lett. 77, 793-797 (1996).
[CrossRef] [PubMed]

Suominen, K. A.

G. M. Palma, K. A. Suominen, and A. K. Ekert, “Quantum computers and dissipation,” arXiv:quant-ph/9702001v/.

Terhal, B. M.

C. H. Bennett, D. P. DiCincenzo, P. W. Shor, J. A. Smolin, B. M. Terhal, and W. K. Wotters, “Remote state preparation,” Phys. Rev. Lett. 87, 077902 (2001).
[CrossRef] [PubMed]

Tittel, W.

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

Viola, L.

L. Viola, E. Knill, and S. Lloyd, “Dynamical decoupling of open quantum systems,” Phys. Rev. Lett. 82, 2417-2421 (1999).
[CrossRef]

Wang, X. B.

X. B. Wang, “Quantum key distribution with two-qubit quantum codes,” Phys. Rev. Lett. 92, 077902 (2004).
[CrossRef] [PubMed]

Weihs, G.

J. W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435-4438 (2001).
[CrossRef] [PubMed]

Weinfurter, H.

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
[CrossRef] [PubMed]

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]

J. W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature (London) 403, 515-519 (2000).
[CrossRef]

D. Bouwmeester, J. W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345-1349 (1999).
[CrossRef]

Wendelken, S. M.

J. B. Altepeter, P. G. Hadley, S. M. Wendelken, A. J. Berglund, and P. G. Kwiat, “Experimental investigation of a two-qubit decoherence-free subspace,” Phys. Rev. Lett. 92, 147901 (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]

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. 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]

Wotters, W. K.

C. H. Bennett, D. P. DiCincenzo, P. W. Shor, J. A. Smolin, B. M. Terhal, and W. K. Wotters, “Remote state preparation,” Phys. Rev. Lett. 87, 077902 (2001).
[CrossRef] [PubMed]

Wu, W.

W. T. Liu, W. Wu, B. Q. Ou, P. X. Chen, C. Z. Li, and J. M. Yuan, “Experimental remote preparation of arbitrary photon polarization states,” Phys. Rev. A 76, 022308 (2007).
[CrossRef]

Xia, Y.

Y. Xia, J. Song, and H. S. Song, “Linear optical protocol for preparation of N-photon Greenberger-Horne-Zeilinger state with conventional photon detectors,” Appl. Phys. Lett. 92, 021128 (2008).
[CrossRef]

Yanmamoto, Y.

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

Yuan, J. M.

W. T. Liu, W. Wu, B. Q. Ou, P. X. Chen, C. Z. Li, and J. M. Yuan, “Experimental remote preparation of arbitrary photon polarization states,” Phys. Rev. A 76, 022308 (2007).
[CrossRef]

Zanardi, P.

P. Zanardi and M. Rasetti, “Noiseless quantum codes,” Phys. Rev. Lett. 79, 3306-3309 (1997).
[CrossRef]

Zbinden, H.

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

Zeilinger, A.

J. W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435-4438 (2001).
[CrossRef] [PubMed]

J. W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature (London) 403, 515-519 (2000).
[CrossRef]

D. Bouwmeester, J. W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345-1349 (1999).
[CrossRef]

Zhang, S. L.

X. B. Zou, S. L. Zhang, K. L. 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]

Zou, X. B.

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, S. L. Zhang, K. L. 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, 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]

Zurek, W. H.

R. Laflamme, C. Miquel, J. P. Paz, and W. H. Zurek, “Perfect quantum error correcting code,” Phys. Rev. Lett. 77, 198-201 (1996).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

Y. Xia, J. Song, and H. S. Song, “Linear optical protocol for preparation of N-photon Greenberger-Horne-Zeilinger state with conventional photon detectors,” Appl. Phys. Lett. 92, 021128 (2008).
[CrossRef]

Nature (London) (1)

J. W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature (London) 403, 515-519 (2000).
[CrossRef]

Phys. Rev. A (11)

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]

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

T. B. Pittman, B. C. Jacobs, J. D. Franson, “Probabilistic quantum encoder for single-photon qubits,” Phys. Rev. A 69, 042306 (2004).
[CrossRef]

X. B. Zou, S. L. Zhang, K. L. 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]

W. T. Liu, W. Wu, B. Q. Ou, P. X. Chen, C. Z. Li, and J. M. Yuan, “Experimental remote preparation of arbitrary photon polarization states,” Phys. Rev. A 76, 022308 (2007).
[CrossRef]

F. G. Deng and G. L. Long, “Controlled order rearrangement encryption for quantum key distribution,” Phys. Rev. A 68, 042315 (2003).
[CrossRef]

P. W. Shor, “Scheme for reducing decoherence in quantum computer memory,” Phys. Rev. A 52, R2493-R2496 (1995).
[CrossRef] [PubMed]

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]

A. Cabello, “Greenberger-Horne-Zeilinger-like proof of Bells theorem involving observers who do not share a reference frame,” Phys. Rev. A 68, 042104 (2003).
[CrossRef]

Phys. Rev. Lett. (19)

A. Cabello, “Bells theorem without inequalities and without alignments,” Phys. Rev. Lett. 91, 230403 (2004).
[CrossRef]

S. D. Bartlett, T. Rudolph, and R. W. Spekkens, “Classical and quantum communication without a shared reference frame,” Phys. Rev. Lett. 91, 027901 (2003).
[CrossRef] [PubMed]

J. C. Boileau, D. Gottesman, R. Laflamme, D. Poulin, and R. W. Spekkens, “Robust polarization-based quantum key distribution over a collective-noise channel,” Phys. Rev. Lett. 92, 017901 (2004).
[CrossRef] [PubMed]

L. M. Duan and G. C. Guo, “Preserving coherence in quantum computation by pairing quantum bits,” Phys. Rev. Lett. 79, 1953-1956 (1997).
[CrossRef]

P. Zanardi and M. Rasetti, “Noiseless quantum codes,” Phys. Rev. Lett. 79, 3306-3309 (1997).
[CrossRef]

J. B. Altepeter, P. G. Hadley, S. M. Wendelken, A. J. Berglund, and P. G. Kwiat, “Experimental investigation of a two-qubit decoherence-free subspace,” Phys. Rev. Lett. 92, 147901 (2004).
[CrossRef] [PubMed]

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]

A. M. Steane, “Error correcting codes in quantum theory,” Phys. Rev. Lett. 77, 793-797 (1996).
[CrossRef] [PubMed]

R. Laflamme, C. Miquel, J. P. Paz, and W. H. Zurek, “Perfect quantum error correcting code,” Phys. Rev. Lett. 77, 198-201 (1996).
[CrossRef] [PubMed]

L. Viola, E. Knill, and S. Lloyd, “Dynamical decoupling of open quantum systems,” Phys. Rev. Lett. 82, 2417-2421 (1999).
[CrossRef]

X. B. Wang, “Quantum key distribution with two-qubit quantum codes,” Phys. Rev. Lett. 92, 077902 (2004).
[CrossRef] [PubMed]

C. H. Bennett, D. P. DiCincenzo, P. W. Shor, J. A. Smolin, B. M. Terhal, and W. K. Wotters, “Remote state preparation,” Phys. Rev. Lett. 87, 077902 (2001).
[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]

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]

D. Bouwmeester, J. W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345-1349 (1999).
[CrossRef]

J. W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435-4438 (2001).
[CrossRef] [PubMed]

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

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]

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

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

Other (1)

G. M. Palma, K. A. Suominen, and A. K. Ekert, “Quantum computers and dissipation,” arXiv:quant-ph/9702001v/.

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Figures (2)

Fig. 1
Fig. 1

Schematic for realizing controlled encoding transformation. PBS denotes the polarization beam splitter, HWP denotes the half-wave plate, P denotes the π 2 -phase shift, and D 1 ( 2 ) are detectors.

Fig. 2
Fig. 2

Schematic for controlled generation of four-photon polarization entangled decoherence-free states. F denotes the setup shown in Fig. 1. BS denotes the beam splitter.

Equations (16)

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

Φ 0 = α ψ 0 + β ψ 1 ,
ψ 0 = 1 2 ( H 1 V 2 V 1 H 2 ) ( H 3 V 4 V 3 H 4 ) ,
ψ 1 = 1 2 3 ( 2 V 1 V 2 H 3 H 4 + 2 H 1 H 2 V 3 V 4 V 1 H 2 V 3 H 4 V 1 H 2 H 3 V 4 H 1 V 2 H 3 V 4 H 1 V 2 V 3 H 4 ) ,
ψ in = γ H + δ V ,
Ψ = ( γ H + δ V ) 0 ( 1 2 ( H V + V H ) ) 12 PBS 1 , HWP , PBS 2 1 2 [ H b ( γ H V + δ V H ) 1 2 + V c ( γ H V δ V H ) 1 2 ] + 1 2 γ H V 1 H 2 + 1 2 δ ( 2 H b 2 V c ) V 2 ,
Ψ out 1 = γ H V 1 2 δ V H 1 2 ,
Ψ out 2 = γ H V 1 2 + δ V H 1 2 ,
Φ in = Ψ in 1 Ψ in 2 = ( γ H + δ V ) ( γ 1 H + δ 1 V ) ,
Ψ 1 Ψ 2 = ( γ H V + δ V H ) p 1 p 2 ( γ 1 H V + δ 1 V H ) p 3 p 4 .
a P 2 , j + ( cos θ ) a P 2 , j + + ( sin θ ) a P 3 , j + ,
a P 3 , j + ( cos θ ) a P 3 , j + ( sin θ ) a P 2 , j + ,
Ψ mix = γ γ 1 cos 2 θ H p 1 V p 2 H p 3 V p 4 γ γ 1 cos 2 θ H p 1 V p 2 V p 3 H p 4 + δ δ 1 sin 2 θ H p 1 H p 2 V p 3 V p 4 + δ δ 1 sin 2 θ H p 1 V p 2 V p 3 H p 4 γ γ 1 cos 2 θ V p 1 H p 2 V p 3 V p 4 + γ γ 1 cos 2 θ V p 1 H p 2 V p 3 H p 4 + δ δ 1 sin 2 θ V p 1 H p 2 V p 3 V p 4 δ δ 1 sin 2 θ V p 1 V p 2 H p 3 H p 4 = γ γ 1 cos 2 θ ( H p 1 V p 2 V p 1 H p 2 ) ( H p 3 V p 4 V p 3 H p 4 ) δ δ 1 sin 2 θ ( H p 1 V p 3 V p 1 H p 3 ) ( H p 2 V p 4 V p 2 H p 4 ) ,
Ψ mix = ( γ γ 1 cos 2 θ 1 2 δ δ 1 sin 2 θ ) ( H p 1 V p 2 V p 1 H p 2 ) ( H p 3 V p 4 V p 3 H p 4 ) δ δ 1 sin 2 θ [ V p 1 V p 2 H p 3 H p 4 + H p 1 H p 2 V p 3 V p 4 1 2 ( H p 1 V p 2 + V p 1 H p 2 ) ( H p 3 V p 4 + V p 3 H p 4 ) ] = 1 2 γ 2 γ 1 2 cos 4 θ γ γ 1 δ δ 1 cos 2 θ sin 2 θ + δ δ 1 2 sin 4 θ × { [ 2 γ γ 1 ( 2 γ γ 1 + δ δ 1 ) sin 2 θ ] ψ 0 3 δ δ 1 sin 2 θ ψ 1 } ,
P = ( η [ 1 + δ 2 ( 2 η ) ] ) 2 ( γ 2 γ 1 2 cos 4 θ + δ 2 δ 1 2 sin 4 θ ) 4 [ γ 2 γ 1 2 cos 4 θ + δ 2 δ 1 2 sin 4 θ + ( γ 2 δ 1 2 + γ 1 2 δ 2 ) cos 2 θ sin 2 θ ] .
α = 2 γ γ 1 ( 2 γ γ 1 + δ δ 1 ) sin 2 θ 2 γ 2 γ 1 2 cos 4 θ γ γ 1 δ δ 1 cos 2 θ sin 2 θ + δ 2 δ 1 2 sin 4 θ ,
β = 3 δ δ 1 sin 2 θ 2 γ 2 γ 1 2 cos 4 θ γ γ 1 δ δ 1 cos 2 θ sin 2 θ + δ 2 δ 1 2 sin 4 θ .

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