Abstract

We propose a protocol to generate a class of entangled states of N Λ-type three-level atoms trapped in distant cavities by using interference of polarized photons. The proposed setup involves simple linear optical elements, cavities, and the conventional photon detectors that only distinguish the vacuum and the nonvacuum Fock number states.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  5. 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]
  6. 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]
  7. A. Ekert, “Quantum cryptography based on Bell's theorem,” Phys. Rev. Lett. 67, 661-663 (1991).
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  8. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145-149 (2002).
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  9. N. Gisin and S. Massar, “Optimal quantum cloning machines,” Phys. Rev. Lett. 79, 2153-2156 (1997).
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  11. S. Bose, P. L. Knight, M. B. Plenio, and V. Vedral, “Proposal for teleportation of an atomic state via cavity decay,” Phys. Rev. Lett. 83, 5158-5161 (1999).
    [CrossRef]
  12. X. L. Feng, Z. M. Zhang, X. D. Li, S. Q. Li, S. Q. Gong, and Z. Z. Xu, “Entangling distant atoms by interference of polarized photons,” Phys. Rev. Lett. 90, 217902 (2003).
    [CrossRef] [PubMed]
  13. L. M. Duan and H. J. Kimble, “Efficient engineering of multiatom entanglement through single-photon detections,” Phys. Rev. Lett. 90, 253601 (2003).
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  14. X. Zou, K. Pahlke, and W. Mathis, “Conditional generation of the Greenberger-Horne-Zeilinger state of four distant atoms via cavity decay,” Phys. Rev. A 68, 024302 (2003).
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  15. S. D. Barrett and P. Kok, “Efficient high-fidelity quantum computation using matter qubits and linear optics,” Phys. Rev. A 71, 060310(R) (2005).
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  16. Y. L. Lim, A. Beige, and L. C. Kwek, “Efficient high-fidelity quantum computation using matter qubits and linear optics,” Phys. Rev. Lett. 95, 030505 (2005).
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  17. S. J. Devitt, A. D. Greentree, R. Lonicioiu, J. L. O'Brien, W. J. Munro, and L. C. L. Hollenberg, “Photonic module: an on-demand resource for photonic entanglement,” Phys. Rev. A 76, 052312 (2007).
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  18. X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, “Experimental preparation of quadripartite cluster and Greenberger-Horne-Zeilinger entangled states for continuous variables,” Phys. Rev. Lett. 98, 070502 (2007).
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    [CrossRef]
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    [CrossRef] [PubMed]
  23. Y. Xia, J. Song, H. S. Song, and S. Zhang, “Controlled generation of four-photon polarization-entangled decoherence-free states with conventional photon detectors,” J. Opt. Soc. Am. B 26, 129-132 (2009).
    [CrossRef]
  24. H. J. Briegel and R. Raussendorf, “Persistent entanglement in arrays of interacting particles,” Phys. Rev. Lett. 86, 910-913 (2001).
    [CrossRef] [PubMed]
  25. W. Dur and H. J. Briegel, “Stability of macroscopic entanglement under decoherence,” Phys. Rev. Lett. 92, 180403 (2004).
    [CrossRef] [PubMed]
  26. V. Scarani, A. Acin, E. Schenck, and M. Aspelmeyer, “Nonlocality of cluster states of qubits,” Phys. Rev. A 71, 042325 (2005).
    [CrossRef]
  27. R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Phys. Rev. Lett. 86, 5188 (2001).
    [CrossRef] [PubMed]
  28. T. Tanamoto, Y. X. Liu, X. D. Hu, and F. Nori, “Efficient quantum circuits for one-way quantum computing,” Phys. Rev. Lett. 102, 100501 (2009).
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    [CrossRef]
  30. X. B. Zou and W. Mathis, “Schemes for generating the cluster states in microwave cavity QED,” Phys. Rev. A 72, 013809 (2005).
    [CrossRef]
  31. S. B. Zheng, “Generation of cluster states in ion-trap systems,” Phys. Rev. A 73, 065802 (2006).
    [CrossRef]
  32. Z. J. Deng, M. Feng, and K. L. Gao, “Preparation of entangled states of four remote atomic qubits in decoherence-free subspace,” Phys. Rev. A 75, 024302 (2007).
    [CrossRef]
  33. L. Jiang, A. M. Rey, O. Romero-Isart, J. J. García-Ripoll, A. Sanpera, and M. D. Lukin, “Preparation of decoherence-free cluster states with optical superlattices,” Phys. Rev. A 79, 022309 (2009).
    [CrossRef]
  34. W. Lange and H. J. Kimble, “Dynamic generation of maximally entangled photon multiplets by adiabatic passage,” Phys. Rev. A 61, 063817 (2000).
    [CrossRef]
  35. X. H. Li, F. G. Deng, and H. Y. Zhou, “Faithful qubit transmission against collective noise without ancillary qubits,” Appl. Phys. Lett. 91, 144101 (2007).
    [CrossRef]
  36. X. B. Wang, T. Hiroshima, A. Tomita, and M. Hayashi, “Quantum information with Gaussian states,” Phys. Rep. 448, 1 (2007).
    [CrossRef]
  37. X. B. Wang, “Qutrit state engineering with biphotons,” Phys. Rev. Lett. 94, 230503 (2005).
    [CrossRef] [PubMed]
  38. 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 403, 515-519 (2000).
    [CrossRef] [PubMed]
  39. S. Chen, Y. A. Chen, B. Zhao, Z. S. Yuan, J. Schmiedmayer, and J. W. Pan, “Demonstration of a stable atom-photon entanglement source for quantum repeaters,” Phys. Rev. Lett. 99, 180505 (2007).
    [CrossRef] [PubMed]
  40. A. Imamoglu, “High efficiency photon counting using stored light,” Phys. Rev. Lett. 89, 163602 (2002).
    [CrossRef] [PubMed]
  41. D. F. V. James and P. G. Kwiat, “Atomic-vapor-based high efficiency optical detectors with photon number resolution,” Phys. Rev. Lett. 89, 183601 (2002).
    [CrossRef] [PubMed]
  42. J. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, “Multiphoton detection using visible light photon counter,” Appl. Phys. Lett. 74, 902-904 (1999).
    [CrossRef]

2009 (5)

T. Bastin, C. Thiel, J. von Zanthier, L. Lamata, E. Solano, and G. S. Agarwal, “Operational determination of multiqubit entanglement classes via tuning of local operations,” Phys. Rev. Lett. 102, 053601 (2009).
[CrossRef] [PubMed]

Y. Xia, J. Song, H. S. Song, and S. Zhang, “Controlled generation of four-photon polarization-entangled decoherence-free states with conventional photon detectors,” J. Opt. Soc. Am. B 26, 129-132 (2009).
[CrossRef]

T. Tanamoto, Y. X. Liu, X. D. Hu, and F. Nori, “Efficient quantum circuits for one-way quantum computing,” Phys. Rev. Lett. 102, 100501 (2009).
[CrossRef] [PubMed]

M. Rosenkranz and D. Jaksch, “Parameter estimation with cluster states,” Phys. Rev. A 79, 022103 (2009).
[CrossRef]

L. Jiang, A. M. Rey, O. Romero-Isart, J. J. García-Ripoll, A. Sanpera, and M. D. Lukin, “Preparation of decoherence-free cluster states with optical superlattices,” Phys. Rev. A 79, 022309 (2009).
[CrossRef]

2008 (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, 021127 (2008).
[CrossRef]

2007 (8)

X. H. Li, F. G. Deng, and H. Y. Zhou, “Faithful qubit transmission against collective noise without ancillary qubits,” Appl. Phys. Lett. 91, 144101 (2007).
[CrossRef]

X. B. Wang, T. Hiroshima, A. Tomita, and M. Hayashi, “Quantum information with Gaussian states,” Phys. Rep. 448, 1 (2007).
[CrossRef]

S. J. Devitt, A. D. Greentree, R. Lonicioiu, J. L. O'Brien, W. J. Munro, and L. C. L. Hollenberg, “Photonic module: an on-demand resource for photonic entanglement,” Phys. Rev. A 76, 052312 (2007).
[CrossRef]

X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, “Experimental preparation of quadripartite cluster and Greenberger-Horne-Zeilinger entangled states for continuous variables,” Phys. Rev. Lett. 98, 070502 (2007).
[CrossRef] [PubMed]

C. S. Yu, X. X. Yi, H. S. Song, and D. Mei, “Robust preparation of Greenberger-Horne-Zeilinger and W states of three distant atoms,” Phys. Rev. A 75, 044301 (2007).
[CrossRef]

C. Thiel, J. von Zanthier, T. Bastin, E. Solano, and G. S. Agarwal, “Generation of symmetric dicke states of remote qubits with linear optics,” Phys. Rev. Lett. 99, 193602 (2007).
[CrossRef]

S. Chen, Y. A. Chen, B. Zhao, Z. S. Yuan, J. Schmiedmayer, and J. W. Pan, “Demonstration of a stable atom-photon entanglement source for quantum repeaters,” Phys. Rev. Lett. 99, 180505 (2007).
[CrossRef] [PubMed]

Z. J. Deng, M. Feng, and K. L. Gao, “Preparation of entangled states of four remote atomic qubits in decoherence-free subspace,” Phys. Rev. A 75, 024302 (2007).
[CrossRef]

2006 (1)

S. B. Zheng, “Generation of cluster states in ion-trap systems,” Phys. Rev. A 73, 065802 (2006).
[CrossRef]

2005 (5)

X. B. Wang, “Qutrit state engineering with biphotons,” Phys. Rev. Lett. 94, 230503 (2005).
[CrossRef] [PubMed]

X. B. Zou and W. Mathis, “Schemes for generating the cluster states in microwave cavity QED,” Phys. Rev. A 72, 013809 (2005).
[CrossRef]

V. Scarani, A. Acin, E. Schenck, and M. Aspelmeyer, “Nonlocality of cluster states of qubits,” Phys. Rev. A 71, 042325 (2005).
[CrossRef]

S. D. Barrett and P. Kok, “Efficient high-fidelity quantum computation using matter qubits and linear optics,” Phys. Rev. A 71, 060310(R) (2005).
[CrossRef]

Y. L. Lim, A. Beige, and L. C. Kwek, “Efficient high-fidelity quantum computation using matter qubits and linear optics,” Phys. Rev. Lett. 95, 030505 (2005).
[CrossRef] [PubMed]

2004 (2)

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]

W. Dur and H. J. Briegel, “Stability of macroscopic entanglement under decoherence,” Phys. Rev. Lett. 92, 180403 (2004).
[CrossRef] [PubMed]

2003 (3)

X. L. Feng, Z. M. Zhang, X. D. Li, S. Q. Li, S. Q. Gong, and Z. Z. Xu, “Entangling distant atoms by interference of polarized photons,” Phys. Rev. Lett. 90, 217902 (2003).
[CrossRef] [PubMed]

L. M. Duan and H. J. Kimble, “Efficient engineering of multiatom entanglement through single-photon detections,” Phys. Rev. Lett. 90, 253601 (2003).
[CrossRef] [PubMed]

X. Zou, K. Pahlke, and W. Mathis, “Conditional generation of the Greenberger-Horne-Zeilinger state of four distant atoms via cavity decay,” Phys. Rev. A 68, 024302 (2003).
[CrossRef]

2002 (3)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145-149 (2002).
[CrossRef]

A. Imamoglu, “High efficiency photon counting using stored light,” Phys. Rev. Lett. 89, 163602 (2002).
[CrossRef] [PubMed]

D. F. V. James and P. G. Kwiat, “Atomic-vapor-based high efficiency optical detectors with photon number resolution,” Phys. Rev. Lett. 89, 183601 (2002).
[CrossRef] [PubMed]

2001 (2)

R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Phys. Rev. Lett. 86, 5188 (2001).
[CrossRef] [PubMed]

H. J. Briegel and R. Raussendorf, “Persistent entanglement in arrays of interacting particles,” Phys. Rev. Lett. 86, 910-913 (2001).
[CrossRef] [PubMed]

2000 (3)

W. Lange and H. J. Kimble, “Dynamic generation of maximally entangled photon multiplets by adiabatic passage,” Phys. Rev. A 61, 063817 (2000).
[CrossRef]

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 403, 515-519 (2000).
[CrossRef] [PubMed]

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

1999 (3)

C. Cabrillo, J. I. Cirac, P. Garcia-Fernandez, and P. Zoller, “Creation of entangled states of distant atoms by interference,” Phys. Rev. A 59, 1025-1033 (1999).
[CrossRef]

S. Bose, P. L. Knight, M. B. Plenio, and V. Vedral, “Proposal for teleportation of an atomic state via cavity decay,” Phys. Rev. Lett. 83, 5158-5161 (1999).
[CrossRef]

J. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, “Multiphoton detection using visible light photon counter,” Appl. Phys. Lett. 74, 902-904 (1999).
[CrossRef]

1997 (1)

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

1993 (1)

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

1992 (1)

D. Deutsch and R. Jozsa, “Rapid solution of problems by quantum computation,” Proc. R. Soc. London, Ser. A 439, 553-558 (1992).
[CrossRef]

1991 (1)

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

1990 (1)

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, “Bells theorem without inequalities,” Am. J. Phys. 58, 1131-1143 (1990).
[CrossRef]

Acin, A.

V. Scarani, A. Acin, E. Schenck, and M. Aspelmeyer, “Nonlocality of cluster states of qubits,” Phys. Rev. A 71, 042325 (2005).
[CrossRef]

Agarwal, G. S.

T. Bastin, C. Thiel, J. von Zanthier, L. Lamata, E. Solano, and G. S. Agarwal, “Operational determination of multiqubit entanglement classes via tuning of local operations,” Phys. Rev. Lett. 102, 053601 (2009).
[CrossRef] [PubMed]

C. Thiel, J. von Zanthier, T. Bastin, E. Solano, and G. S. Agarwal, “Generation of symmetric dicke states of remote qubits with linear optics,” Phys. Rev. Lett. 99, 193602 (2007).
[CrossRef]

Aspelmeyer, M.

V. Scarani, A. Acin, E. Schenck, and M. Aspelmeyer, “Nonlocality of cluster states of qubits,” Phys. Rev. A 71, 042325 (2005).
[CrossRef]

Barrett, S. D.

S. D. Barrett and P. Kok, “Efficient high-fidelity quantum computation using matter qubits and linear optics,” Phys. Rev. A 71, 060310(R) (2005).
[CrossRef]

Bastin, T.

T. Bastin, C. Thiel, J. von Zanthier, L. Lamata, E. Solano, and G. S. Agarwal, “Operational determination of multiqubit entanglement classes via tuning of local operations,” Phys. Rev. Lett. 102, 053601 (2009).
[CrossRef] [PubMed]

C. Thiel, J. von Zanthier, T. Bastin, E. Solano, and G. S. Agarwal, “Generation of symmetric dicke states of remote qubits with linear optics,” Phys. Rev. Lett. 99, 193602 (2007).
[CrossRef]

Beige, A.

Y. L. Lim, A. Beige, and L. C. Kwek, “Efficient high-fidelity quantum computation using matter qubits and linear optics,” Phys. Rev. Lett. 95, 030505 (2005).
[CrossRef] [PubMed]

Bennett, C. H.

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]

Bidal, G.

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

Bose, S.

S. Bose, P. L. Knight, M. B. Plenio, and V. Vedral, “Proposal for teleportation of an atomic state via cavity decay,” Phys. Rev. Lett. 83, 5158-5161 (1999).
[CrossRef]

Bourennane, M.

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 403, 515-519 (2000).
[CrossRef] [PubMed]

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]

Briegel, H. J.

W. Dur and H. J. Briegel, “Stability of macroscopic entanglement under decoherence,” Phys. Rev. Lett. 92, 180403 (2004).
[CrossRef] [PubMed]

R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Phys. Rev. Lett. 86, 5188 (2001).
[CrossRef] [PubMed]

H. J. Briegel and R. Raussendorf, “Persistent entanglement in arrays of interacting particles,” Phys. Rev. Lett. 86, 910-913 (2001).
[CrossRef] [PubMed]

Cabrillo, C.

C. Cabrillo, J. I. Cirac, P. Garcia-Fernandez, and P. Zoller, “Creation of entangled states of distant atoms by interference,” Phys. Rev. A 59, 1025-1033 (1999).
[CrossRef]

Chen, S.

S. Chen, Y. A. Chen, B. Zhao, Z. S. Yuan, J. Schmiedmayer, and J. W. Pan, “Demonstration of a stable atom-photon entanglement source for quantum repeaters,” Phys. Rev. Lett. 99, 180505 (2007).
[CrossRef] [PubMed]

Chen, Y. A.

S. Chen, Y. A. Chen, B. Zhao, Z. S. Yuan, J. Schmiedmayer, and J. W. Pan, “Demonstration of a stable atom-photon entanglement source for quantum repeaters,” Phys. Rev. Lett. 99, 180505 (2007).
[CrossRef] [PubMed]

Cirac, J. I.

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

C. Cabrillo, J. I. Cirac, P. Garcia-Fernandez, and P. Zoller, “Creation of entangled states of distant atoms by interference,” Phys. Rev. A 59, 1025-1033 (1999).
[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, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature 403, 515-519 (2000).
[CrossRef] [PubMed]

Deng, F. G.

X. H. Li, F. G. Deng, and H. Y. Zhou, “Faithful qubit transmission against collective noise without ancillary qubits,” Appl. Phys. Lett. 91, 144101 (2007).
[CrossRef]

Deng, Z. J.

Z. J. Deng, M. Feng, and K. L. Gao, “Preparation of entangled states of four remote atomic qubits in decoherence-free subspace,” Phys. Rev. A 75, 024302 (2007).
[CrossRef]

Deutsch, D.

D. Deutsch and R. Jozsa, “Rapid solution of problems by quantum computation,” Proc. R. Soc. London, Ser. A 439, 553-558 (1992).
[CrossRef]

Devitt, S. J.

S. J. Devitt, A. D. Greentree, R. Lonicioiu, J. L. O'Brien, W. J. Munro, and L. C. L. Hollenberg, “Photonic module: an on-demand resource for photonic entanglement,” Phys. Rev. A 76, 052312 (2007).
[CrossRef]

Duan, L. M.

L. M. Duan and H. J. Kimble, “Efficient engineering of multiatom entanglement through single-photon detections,” Phys. Rev. Lett. 90, 253601 (2003).
[CrossRef] [PubMed]

Dur, W.

W. Dur and H. J. Briegel, “Stability of macroscopic entanglement under decoherence,” Phys. Rev. Lett. 92, 180403 (2004).
[CrossRef] [PubMed]

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

Eibl, M.

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.

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

Feng, M.

Z. J. Deng, M. Feng, and K. L. Gao, “Preparation of entangled states of four remote atomic qubits in decoherence-free subspace,” Phys. Rev. A 75, 024302 (2007).
[CrossRef]

Feng, X. L.

X. L. Feng, Z. M. Zhang, X. D. Li, S. Q. Li, S. Q. Gong, and Z. Z. Xu, “Entangling distant atoms by interference of polarized photons,” Phys. Rev. Lett. 90, 217902 (2003).
[CrossRef] [PubMed]

Gao, K. L.

Z. J. Deng, M. Feng, and K. L. Gao, “Preparation of entangled states of four remote atomic qubits in decoherence-free subspace,” Phys. Rev. A 75, 024302 (2007).
[CrossRef]

Garcia-Fernandez, P.

C. Cabrillo, J. I. Cirac, P. Garcia-Fernandez, and P. Zoller, “Creation of entangled states of distant atoms by interference,” Phys. Rev. A 59, 1025-1033 (1999).
[CrossRef]

García-Ripoll, J. J.

L. Jiang, A. M. Rey, O. Romero-Isart, J. J. García-Ripoll, A. Sanpera, and M. D. Lukin, “Preparation of decoherence-free cluster states with optical superlattices,” Phys. Rev. A 79, 022309 (2009).
[CrossRef]

Gisin, N.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145-149 (2002).
[CrossRef]

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

Gong, S. Q.

X. L. Feng, Z. M. Zhang, X. D. Li, S. Q. Li, S. Q. Gong, and Z. Z. Xu, “Entangling distant atoms by interference of polarized photons,” Phys. Rev. Lett. 90, 217902 (2003).
[CrossRef] [PubMed]

Greenberger, D. M.

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L. Jiang, A. M. Rey, O. Romero-Isart, J. J. García-Ripoll, A. Sanpera, and M. D. Lukin, “Preparation of decoherence-free cluster states with optical superlattices,” Phys. Rev. A 79, 022309 (2009).
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S. J. Devitt, A. D. Greentree, R. Lonicioiu, J. L. O'Brien, W. J. Munro, and L. C. L. Hollenberg, “Photonic module: an on-demand resource for photonic entanglement,” Phys. Rev. A 76, 052312 (2007).
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S. Chen, Y. A. Chen, B. Zhao, Z. S. Yuan, J. Schmiedmayer, and J. W. Pan, “Demonstration of a stable atom-photon entanglement source for quantum repeaters,” Phys. Rev. Lett. 99, 180505 (2007).
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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 403, 515-519 (2000).
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Peng, K.

X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, “Experimental preparation of quadripartite cluster and Greenberger-Horne-Zeilinger entangled states for continuous variables,” Phys. Rev. Lett. 98, 070502 (2007).
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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).
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S. Bose, P. L. Knight, M. B. Plenio, and V. Vedral, “Proposal for teleportation of an atomic state via cavity decay,” Phys. Rev. Lett. 83, 5158-5161 (1999).
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L. Jiang, A. M. Rey, O. Romero-Isart, J. J. García-Ripoll, A. Sanpera, and M. D. Lukin, “Preparation of decoherence-free cluster states with optical superlattices,” Phys. Rev. A 79, 022309 (2009).
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N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145-149 (2002).
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L. Jiang, A. M. Rey, O. Romero-Isart, J. J. García-Ripoll, A. Sanpera, and M. D. Lukin, “Preparation of decoherence-free cluster states with optical superlattices,” Phys. Rev. A 79, 022309 (2009).
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Rosenkranz, M.

M. Rosenkranz and D. Jaksch, “Parameter estimation with cluster states,” Phys. Rev. A 79, 022103 (2009).
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Sanpera, A.

L. Jiang, A. M. Rey, O. Romero-Isart, J. J. García-Ripoll, A. Sanpera, and M. D. Lukin, “Preparation of decoherence-free cluster states with optical superlattices,” Phys. Rev. A 79, 022309 (2009).
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V. Scarani, A. Acin, E. Schenck, and M. Aspelmeyer, “Nonlocality of cluster states of qubits,” Phys. Rev. A 71, 042325 (2005).
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S. Chen, Y. A. Chen, B. Zhao, Z. S. Yuan, J. Schmiedmayer, and J. W. Pan, “Demonstration of a stable atom-photon entanglement source for quantum repeaters,” Phys. Rev. Lett. 99, 180505 (2007).
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D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, “Bells theorem without inequalities,” Am. J. Phys. 58, 1131-1143 (1990).
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T. Bastin, C. Thiel, J. von Zanthier, L. Lamata, E. Solano, and G. S. Agarwal, “Operational determination of multiqubit entanglement classes via tuning of local operations,” Phys. Rev. Lett. 102, 053601 (2009).
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C. Thiel, J. von Zanthier, T. Bastin, E. Solano, and G. S. Agarwal, “Generation of symmetric dicke states of remote qubits with linear optics,” Phys. Rev. Lett. 99, 193602 (2007).
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Y. Xia, J. Song, H. S. Song, and S. Zhang, “Controlled generation of four-photon polarization-entangled decoherence-free states with conventional photon detectors,” J. Opt. Soc. Am. B 26, 129-132 (2009).
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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, 021127 (2008).
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C. S. Yu, X. X. Yi, H. S. Song, and D. Mei, “Robust preparation of Greenberger-Horne-Zeilinger and W states of three distant atoms,” Phys. Rev. A 75, 044301 (2007).
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Song, J.

Y. Xia, J. Song, H. S. Song, and S. Zhang, “Controlled generation of four-photon polarization-entangled decoherence-free states with conventional photon detectors,” J. Opt. Soc. Am. B 26, 129-132 (2009).
[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, 021127 (2008).
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Su, X.

X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, “Experimental preparation of quadripartite cluster and Greenberger-Horne-Zeilinger entangled states for continuous variables,” Phys. Rev. Lett. 98, 070502 (2007).
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J. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, “Multiphoton detection using visible light photon counter,” Appl. Phys. Lett. 74, 902-904 (1999).
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X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, “Experimental preparation of quadripartite cluster and Greenberger-Horne-Zeilinger entangled states for continuous variables,” Phys. Rev. Lett. 98, 070502 (2007).
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T. Tanamoto, Y. X. Liu, X. D. Hu, and F. Nori, “Efficient quantum circuits for one-way quantum computing,” Phys. Rev. Lett. 102, 100501 (2009).
[CrossRef] [PubMed]

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T. Bastin, C. Thiel, J. von Zanthier, L. Lamata, E. Solano, and G. S. Agarwal, “Operational determination of multiqubit entanglement classes via tuning of local operations,” Phys. Rev. Lett. 102, 053601 (2009).
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C. Thiel, J. von Zanthier, T. Bastin, E. Solano, and G. S. Agarwal, “Generation of symmetric dicke states of remote qubits with linear optics,” Phys. Rev. Lett. 99, 193602 (2007).
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N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145-149 (2002).
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X. B. Wang, T. Hiroshima, A. Tomita, and M. Hayashi, “Quantum information with Gaussian states,” Phys. Rep. 448, 1 (2007).
[CrossRef]

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S. Bose, P. L. Knight, M. B. Plenio, and V. Vedral, “Proposal for teleportation of an atomic state via cavity decay,” Phys. Rev. Lett. 83, 5158-5161 (1999).
[CrossRef]

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T. Bastin, C. Thiel, J. von Zanthier, L. Lamata, E. Solano, and G. S. Agarwal, “Operational determination of multiqubit entanglement classes via tuning of local operations,” Phys. Rev. Lett. 102, 053601 (2009).
[CrossRef] [PubMed]

C. Thiel, J. von Zanthier, T. Bastin, E. Solano, and G. S. Agarwal, “Generation of symmetric dicke states of remote qubits with linear optics,” Phys. Rev. Lett. 99, 193602 (2007).
[CrossRef]

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X. B. Wang, T. Hiroshima, A. Tomita, and M. Hayashi, “Quantum information with Gaussian states,” Phys. Rep. 448, 1 (2007).
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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]

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 403, 515-519 (2000).
[CrossRef] [PubMed]

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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]

Xia, Y.

Y. Xia, J. Song, H. S. Song, and S. Zhang, “Controlled generation of four-photon polarization-entangled decoherence-free states with conventional photon detectors,” J. Opt. Soc. Am. B 26, 129-132 (2009).
[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, 021127 (2008).
[CrossRef]

Xie, C.

X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, “Experimental preparation of quadripartite cluster and Greenberger-Horne-Zeilinger entangled states for continuous variables,” Phys. Rev. Lett. 98, 070502 (2007).
[CrossRef] [PubMed]

Xu, Z. Z.

X. L. Feng, Z. M. Zhang, X. D. Li, S. Q. Li, S. Q. Gong, and Z. Z. Xu, “Entangling distant atoms by interference of polarized photons,” Phys. Rev. Lett. 90, 217902 (2003).
[CrossRef] [PubMed]

Yamamoto, Y.

J. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, “Multiphoton detection using visible light photon counter,” Appl. Phys. Lett. 74, 902-904 (1999).
[CrossRef]

Yi, X. X.

C. S. Yu, X. X. Yi, H. S. Song, and D. Mei, “Robust preparation of Greenberger-Horne-Zeilinger and W states of three distant atoms,” Phys. Rev. A 75, 044301 (2007).
[CrossRef]

Yu, C. S.

C. S. Yu, X. X. Yi, H. S. Song, and D. Mei, “Robust preparation of Greenberger-Horne-Zeilinger and W states of three distant atoms,” Phys. Rev. A 75, 044301 (2007).
[CrossRef]

Yuan, Z. S.

S. Chen, Y. A. Chen, B. Zhao, Z. S. Yuan, J. Schmiedmayer, and J. W. Pan, “Demonstration of a stable atom-photon entanglement source for quantum repeaters,” Phys. Rev. Lett. 99, 180505 (2007).
[CrossRef] [PubMed]

Zbinden, H.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145-149 (2002).
[CrossRef]

Zeilinger, A.

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 403, 515-519 (2000).
[CrossRef] [PubMed]

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, “Bells theorem without inequalities,” Am. J. Phys. 58, 1131-1143 (1990).
[CrossRef]

D. M. Greenberger, M. A. Horne, and A. Zeilinger, in Bell's Theorem, Quantum Theory, and Conceptions of the Universe, M.Kafatos, ed. (Kluwer, 1989).

Zhang, J.

X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, “Experimental preparation of quadripartite cluster and Greenberger-Horne-Zeilinger entangled states for continuous variables,” Phys. Rev. Lett. 98, 070502 (2007).
[CrossRef] [PubMed]

Zhang, S.

Zhang, Z. M.

X. L. Feng, Z. M. Zhang, X. D. Li, S. Q. Li, S. Q. Gong, and Z. Z. Xu, “Entangling distant atoms by interference of polarized photons,” Phys. Rev. Lett. 90, 217902 (2003).
[CrossRef] [PubMed]

Zhao, B.

S. Chen, Y. A. Chen, B. Zhao, Z. S. Yuan, J. Schmiedmayer, and J. W. Pan, “Demonstration of a stable atom-photon entanglement source for quantum repeaters,” Phys. Rev. Lett. 99, 180505 (2007).
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S. B. Zheng, “Generation of cluster states in ion-trap systems,” Phys. Rev. A 73, 065802 (2006).
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X. H. Li, F. G. Deng, and H. Y. Zhou, “Faithful qubit transmission against collective noise without ancillary qubits,” Appl. Phys. Lett. 91, 144101 (2007).
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Zou, X.

X. Zou, K. Pahlke, and W. Mathis, “Conditional generation of the Greenberger-Horne-Zeilinger state of four distant atoms via cavity decay,” Phys. Rev. A 68, 024302 (2003).
[CrossRef]

Zou, X. B.

X. B. Zou and W. Mathis, “Schemes for generating the cluster states in microwave cavity QED,” Phys. Rev. A 72, 013809 (2005).
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Am. J. Phys. (1)

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, “Bells theorem without inequalities,” Am. J. Phys. 58, 1131-1143 (1990).
[CrossRef]

Appl. Phys. Lett. (3)

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, 021127 (2008).
[CrossRef]

X. H. Li, F. G. Deng, and H. Y. Zhou, “Faithful qubit transmission against collective noise without ancillary qubits,” Appl. Phys. Lett. 91, 144101 (2007).
[CrossRef]

J. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, “Multiphoton detection using visible light photon counter,” Appl. Phys. Lett. 74, 902-904 (1999).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nature (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 403, 515-519 (2000).
[CrossRef] [PubMed]

Phys. Rep. (1)

X. B. Wang, T. Hiroshima, A. Tomita, and M. Hayashi, “Quantum information with Gaussian states,” Phys. Rep. 448, 1 (2007).
[CrossRef]

Phys. Rev. A (13)

M. Rosenkranz and D. Jaksch, “Parameter estimation with cluster states,” Phys. Rev. A 79, 022103 (2009).
[CrossRef]

X. B. Zou and W. Mathis, “Schemes for generating the cluster states in microwave cavity QED,” Phys. Rev. A 72, 013809 (2005).
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S. B. Zheng, “Generation of cluster states in ion-trap systems,” Phys. Rev. A 73, 065802 (2006).
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Z. J. Deng, M. Feng, and K. L. Gao, “Preparation of entangled states of four remote atomic qubits in decoherence-free subspace,” Phys. Rev. A 75, 024302 (2007).
[CrossRef]

L. Jiang, A. M. Rey, O. Romero-Isart, J. J. García-Ripoll, A. Sanpera, and M. D. Lukin, “Preparation of decoherence-free cluster states with optical superlattices,” Phys. Rev. A 79, 022309 (2009).
[CrossRef]

W. Lange and H. J. Kimble, “Dynamic generation of maximally entangled photon multiplets by adiabatic passage,” Phys. Rev. A 61, 063817 (2000).
[CrossRef]

V. Scarani, A. Acin, E. Schenck, and M. Aspelmeyer, “Nonlocality of cluster states of qubits,” Phys. Rev. A 71, 042325 (2005).
[CrossRef]

C. S. Yu, X. X. Yi, H. S. Song, and D. Mei, “Robust preparation of Greenberger-Horne-Zeilinger and W states of three distant atoms,” Phys. Rev. A 75, 044301 (2007).
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Figures (2)

Fig. 1
Fig. 1

Atomic level structure.

Fig. 2
Fig. 2

Experimental setup for generating N -atom ( N = M + N ) entangled states. The polarizing beam splitter (PBS) transmits the horizontal polarization ( H ) and reflects the vertical polarization ( V ) , and the HWPs action is given by the transformations | H ( 1 / 2 ) ( | H + | V ) and | V ( 1 / 2 ) ( | H | V ) .

Equations (6)

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| Ψ ( t ) = 1 2 ( | g l | V + | g r | H ) ,
| Ψ = 1 2 ( N + M ) [ ( | g r A 1 | H A 1 + | g l A 1 | V A 1 ) ( | g r A M | H A M + | g l A M | V A M ) ] [ ( | g r B 1 | H B 1 + | g l B 1 | V B 1 ) ( | g r B N | H B N + | g l B N | V B N ) ] PBS ( 1 , , N ) , PBS ( 1 , , M ) 1 2 ( N + M ) [ ( | g r A 1 | g r A 2 | H b 2 | H b + | g r A 1 | g l A 2 | H b 2 | V b 2 + | g l A 1 | g r A 2 | V b | H b + | g l A 1 | g l A 2 | V b | V b 2 ) ( | g r A M | H A b M 1 + | g l A M | V A b M ) ] [ ( | g r B 1 | g r B 2 | H 1 | H 2 + | g r B 1 | g l B 2 | H 2 | V 2 + | g l B 1 | g r B 2 | V 1 | H 1 + | g l B 1 | g l B 2 | V 2 | V 1 ) ( | g r B N | H N 1 + | g l B N | V N ) ] ,     M , N = 2 , 3 , , ,
1 2 [ | g r A 1 | g r A 2 | g r A M | H b M | H b M 1 | H b + | g l A 1 | g l A 2 | g l A M | V b M | V b M 1 | V b ] [ | g r B 1 | g r B 2 | g r B N | H N | H N 1 | H 1 + | g l B 1 | g l B 2 | g l B N | V N | V N 1 | V 1 ] .
1 2 2 [ | g r A 1 | g r A 2 | g r A M | H b M | H b M 1 | H b + | g l A 1 | g l A 2 | g l A M | V b M | V b M 1 | V b ] [ | g r B 1 | g r B 2 | g r B N | H N | H N 1 ( | H 0 + | V 0 ) + | g l B 1 | g l B 2 | g l B N | V N | V N 1 ( | H 0 | V 0 ) ] = 1 2 2 [ ( i = 1 M | g r A i ) | H b M | H b M 1 | H b + ( i = 1 M | g l A i ) | V b M | V b M 1 | V b ] [ ( i = 1 N | g r B i ) | H N | H N 1 ( | H 0 + | V 0 ) + ( i = 1 N | g l B i ) | V N | V N 1 ( | H 0 | V 0 ) ] .
1 2 [ ( i = 1 M | g r A i ) ( i = 1 N | g r B i ) | H b M | H b M 1 | H 0 | H N | H N 1 | H 1 + ( i = 1 M | g r A i ) ( i = 1 N | g l B i ) | H b M | H b M 1 | H 0 | V N | V N 1 | H 1 + ( i = 1 M | g l A i ) ( i = 1 N | g r B i ) | V b M | V b M 1 | V 1 | H N | H N 1 | V 0 ( i = 1 M | g l A i ) ( i = 1 N | g l B i ) | V b M | V b M 1 | V 1 | V N | V N 1 | V 0 ] .
1 2 [ ( i = 1 M | g r A i ) ( i = 1 N | g r B i ) + ( i = 1 M | g r A i ) ( i = 1 N | g l B i ) + ( i = 1 M | g l A i ) ( i = 1 N | g r B i ) ( i = 1 M | g l A i ) ( i = 1 N | g l B i ) ] .

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