Abstract

The entangled states analysis is a very important element for quantum information. It is impossible to unambiguously distinguish the three-photon Greenberger–Horne–Zeilinger (GHZ) states in polarization, resorting to linear optical elements only. Here, we propose an efficient scheme to complete three-photon hyperentangled GHZ states analysis (HGSA) with the help of the cross-Kerr nonlinearity. The three-photon HGSA scheme can also be generalized to N-photon hyperentangled GHZ states analysis. We discuss the application of the HGSA in the quantum secure direct communication (QSDC) with polarization and spatial-mode degrees of freedom. The results show that the HGSA not only increase the channel capacity but also ensure the unconditional security in long-distance quantum communication.

© 2012 Optical Society of America

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  42. P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowing, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007.
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  44. B. He, Q. Lin, and C. Simon, “Cross-Kerr nonlinearity between continuous-mode coherent states and single photons,” Phys. Rev. A 83, 053826 (2011).
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    [CrossRef]
  47. J. Gea-Banacloche, “Impossibility of large phase shifts via the giant Kerr effect with single-photon wave packets,” Phys. Rev. A 81, 043823 (2010).
    [CrossRef]
  48. G. J. Pryde, J. L. O’Brien, A. G. White, S. D. Bartlett, and T. C. Ralph, “Measuring a photonic qubit without destroying it,” Phys. Rev. Lett. 92, 190402 (2004).
    [CrossRef]
  49. T. C. Ralph, S. D. Bartlett, J. L. O’Brien, G. J. Pryde, and H. M. Wiseman, “Quantum nondemolition measurements for quantum information,” Phys. Rev. A 73, 012113 (2006).
  50. G. J. Pryde, J. L. O’Brien, A. G. White, T. C. Ralph, and H. M. Wiseman, “Measurement of quantum weak values of photon polarization,” Phys. Rev. Lett. 94, 220405 (2005).
  51. J. S. Jin, C. S. Yu, and H. S. Song, “Nondestructive identification of the Bell diagonal state,” Phys. Rev. A 83, 032109 (2011).
  52. P. Kok, H. Lee, and J. P. Dowling, “Single-photon quantum-nondemolition detectors constructed with linear optics and projective measurements,” Phys. Rev. A 66, 063814 (2002).
    [CrossRef]
  53. H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, “Optimized phase switching using a single-atom nonlinearity,” J. Opt. B 5, 218 (2003).
    [CrossRef]
  54. Q. Lin, B. He, J. A. Bergou, and Y. H. Ren, “Processing multiphoton states through operation on a single photon: methods and applications,” Phys. Rev. A 80, 042311 (2009).
  55. C. Wittmann, U. L. Andersen, M. Takeoka, D. Sych, and G. Leuchs, “Discrimination of binary coherent states using a homodyne detector and a photon number resolving detector,” Phys. Rev. A 81, 062338 (2010).
    [CrossRef]
  56. P. Kok, “Effects of self-phase-modulation on weak nonlinear optical quantum gates,” Phys. Rev. A 77, 013808 (2008).
    [CrossRef]
  57. Q. Lin and B. He, “Single-photon logic gates using minimal resources,” Phys. Rev. A 80, 042310 (2009).

2011 (6)

Y. B. Sheng, F. G. Deng, and G. L. Long, “Multipartite electronic entanglement purification with charge detection,” Phys. Lett. A 375, 396–400 (2011).
[CrossRef]

Y. Xia, J. Song, P. M. Lu, and H. S. Song, “Effective quantum teleportation of an atomic state between two cavities with the cross-Kerr nonlinearity by interference of polarized photons,” J. Appl. Phys. 109, 103111 (2011).

C. W. Yang, C. W. Tsal, and T. Hwang, “Fault tolerant two-step quantum secure direct communication protocol against collective noises,” Sci. China-Phys. Mech. Astron. 54, 496–501 (2011).
[CrossRef]

C. Wang, Y. S. Li, and L. Hao, “Optical implementation of quantum random walks using weak cross-Kerr media,” Chin. Sci. Bull. 56, 2088–2091 (2011).
[CrossRef]

B. He, Q. Lin, and C. Simon, “Cross-Kerr nonlinearity between continuous-mode coherent states and single photons,” Phys. Rev. A 83, 053826 (2011).

J. S. Jin, C. S. Yu, and H. S. Song, “Nondestructive identification of the Bell diagonal state,” Phys. Rev. A 83, 032109 (2011).

2010 (3)

C. Wittmann, U. L. Andersen, M. Takeoka, D. Sych, and G. Leuchs, “Discrimination of binary coherent states using a homodyne detector and a photon number resolving detector,” Phys. Rev. A 81, 062338 (2010).
[CrossRef]

J. Gea-Banacloche, “Impossibility of large phase shifts via the giant Kerr effect with single-photon wave packets,” Phys. Rev. A 81, 043823 (2010).
[CrossRef]

Y. B. Sheng, F. G. Deng, and G. L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A 82, 032318 (2010).

2009 (7)

X. M. Lin, Z. H. Chen, G. W. Lin, X. D. Chen, and B. B. Ni, “Optical Bell state and Greenberger-Horne-Zeilinger-state analyzers through the cavity input-output process,” Opt. Commun. 282, 3371–3374 (2009).
[CrossRef]

S. Ghose, N. Sinclair, S. Debnath, P. Rungta, and R. Stock, “Tripartite entanglement versus tripartite nonlocality in three-qubit Greenberger-Horne-Zeilinger-class states,” Phys. Rev. Lett. 102, 250404 (2009).
[CrossRef]

G. Vallone, R. Ceccarelli, F. De Martini, and P. Mataloni, “Hyperentanglement of two photons in three degrees of freedom,” Phys. Rev. A 79, 030301(R) (2009).
[CrossRef]

G. Vallone, R. Ceccarelli, F. De Martini, and P. Mataloni, “Hyperentanglement of two photons in three degrees of freedom,” Phys. Rev. A 79, 030301(R) (2009).
[CrossRef]

C. Wang, L. Xiao, W. Y. Wang, G. Y. Zhang, and G. L. Long, “Quantum key distribution using polarization and frequency hyperentangled photons,” J. Opt. Soc. Am. B 26, 2072–2076 (2009).

Q. Lin, B. He, J. A. Bergou, and Y. H. Ren, “Processing multiphoton states through operation on a single photon: methods and applications,” Phys. Rev. A 80, 042311 (2009).

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

2008 (4)

P. Kok, “Effects of self-phase-modulation on weak nonlinear optical quantum gates,” Phys. Rev. A 77, 013808 (2008).
[CrossRef]

L. Xiao, C. Wang, W. Zhang, Y. D. Huang, J. D. Peng, and G. L. Long, “Efficient strategy for sharing entanglement via noisy channels with doubly entangled photon pairs,” Phys. Rev. A 77, 042315 (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, 021127 (2008).

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
[CrossRef]

2007 (4)

M. Barbieri, G. Vallone, P. Mataloni, and F. De Martini, “Complete and deterministic discrimination of polarization Bell states assisted by momentum entanglement,” Phys. Rev. A 75, 042317 (2007).
[CrossRef]

Y. Xia and H. S. Song, “Controlled quantum secure direct communication using a non-symmetric quantum channel with quantum superdense coding,” Phys. Lett. A 364, 117–122 (2007).
[CrossRef]

J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Physics 9, 16 (2007).
[CrossRef]

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowing, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007.
[CrossRef]

2006 (7)

J. H. Shapiro, “Single-photon Kerr nonlinearities do not help quantum computation,” Phys. Rev. A 73, 062305 (2006).

T. C. Ralph, S. D. Bartlett, J. L. O’Brien, G. J. Pryde, and H. M. Wiseman, “Quantum nondemolition measurements for quantum information,” Phys. Rev. A 73, 012113 (2006).

X. H. Li, F. G. Deng, and H. Y. Zhou, “Improving the security of secure direct communication based on the secret transmitting order of particles,” Phys. Rev. A 74, 054302 (2006).

C. Schuck, G. Huber, C. Kurtsiefer, and H. Weinfurter, “Complete deterministic linear optics Bell state analysis,” Phys. Rev. Lett. 96, 190501 (2006).
[CrossRef]

G. Gordon and G. Rigolin, “Generalized teleportation protocol,” Phys. Rev. A 73, 042309 (2006).

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).

J. A. W. van Houwelingen, N. Brunner, A. Beveratos, H. Zbinden, and N. Gisin, “Quantum teleportation with a three-Bell-state analyzer,” Phys. Rev. Lett. 96, 130502 (2006).
[CrossRef]

2005 (5)

Z. J. Zhang and Z. X. Man, “Multiparty quantum secret sharing of classical messages based on entanglement swapping,” Phys. Rev. A 72, 022303 (2005).

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of hyperentangled photon pairs,” Phys. Rev. Lett. 95, 260501 (2005).
[CrossRef]

M. Barbieri, C. Cinelli, P. Mataloni, and F. De Martini, “Polarization-momentum hyperentangled states: realization and characterization,” Phys. Rev. A 72, 052110 (2005).
[CrossRef]

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302(R) (2005).

G. J. Pryde, J. L. O’Brien, A. G. White, T. C. Ralph, and H. M. Wiseman, “Measurement of quantum weak values of photon polarization,” Phys. Rev. Lett. 94, 220405 (2005).

2004 (6)

F. G. Deng and G. L. Long, “Secure direct communication with a quantum one-time pad,” Phys. Rev. A 69, 052319 (2004).
[CrossRef]

G. J. Pryde, J. L. O’Brien, A. G. White, S. D. Bartlett, and T. C. Ralph, “Measuring a photonic qubit without destroying it,” Phys. Rev. Lett. 92, 190402 (2004).
[CrossRef]

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
[CrossRef]

L. M. Duan and H. J. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. 92, 127902 (2004).
[CrossRef]

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

R. Ursin, T. Jennewein, M. Aspelmeyer, R. Kaltenbaek, M. Lindenthal, P. Walther, and A. Zeilinger, “Communications: quantum teleportation across the Danube,” Nature 430, 849 (2004).
[CrossRef]

2003 (4)

S. P. Walborn, S. Pádua, and C. H. Monken, “Hyperentanglement-assisted Bell-state analysis,” Phys. Rev. A 68, 042313 (2003).
[CrossRef]

X. B. 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).

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

H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, “Optimized phase switching using a single-atom nonlinearity,” J. Opt. B 5, 218 (2003).
[CrossRef]

2002 (3)

P. Kok, H. Lee, and J. P. Dowling, “Single-photon quantum-nondemolition detectors constructed with linear optics and projective measurements,” Phys. Rev. A 66, 063814 (2002).
[CrossRef]

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

J. Calsamiglia, “Generalized measurements by linear elements,” Phys. Rev. A 65, 030301(R) (2002).
[CrossRef]

1999 (2)

L. Vaidman and N. Yoran, “Methods for reliable teleportation,” Phys. Rev. A 59, 116–125 (1999).
[CrossRef]

N. Lütkenhaus, J. Calsamiglia, and K. A. Suominen, “Bell measurements for teleportation,” Phys. Rev. A 59, 3295–3300 (1999).
[CrossRef]

1998 (1)

P. G. Kwiat and H. Weinfurter, “Embedded Bell-state analysis,” Phys. Rev. A 58, R2623–R2626 (1998).
[CrossRef]

1997 (1)

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

1996 (1)

K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656–4659 (1996).
[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]

1991 (1)

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

Andersen, U. L.

C. Wittmann, U. L. Andersen, M. Takeoka, D. Sych, and G. Leuchs, “Discrimination of binary coherent states using a homodyne detector and a photon number resolving detector,” Phys. Rev. A 81, 062338 (2010).
[CrossRef]

Aspelmeyer, M.

R. Ursin, T. Jennewein, M. Aspelmeyer, R. Kaltenbaek, M. Lindenthal, P. Walther, and A. Zeilinger, “Communications: quantum teleportation across the Danube,” Nature 430, 849 (2004).
[CrossRef]

Barbieri, M.

M. Barbieri, G. Vallone, P. Mataloni, and F. De Martini, “Complete and deterministic discrimination of polarization Bell states assisted by momentum entanglement,” Phys. Rev. A 75, 042317 (2007).
[CrossRef]

M. Barbieri, C. Cinelli, P. Mataloni, and F. De Martini, “Polarization-momentum hyperentangled states: realization and characterization,” Phys. Rev. A 72, 052110 (2005).
[CrossRef]

Barreiro, J. T.

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
[CrossRef]

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of hyperentangled photon pairs,” Phys. Rev. Lett. 95, 260501 (2005).
[CrossRef]

Barrett, S. D.

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302(R) (2005).

Bartlett, S. D.

T. C. Ralph, S. D. Bartlett, J. L. O’Brien, G. J. Pryde, and H. M. Wiseman, “Quantum nondemolition measurements for quantum information,” Phys. Rev. A 73, 012113 (2006).

G. J. Pryde, J. L. O’Brien, A. G. White, S. D. Bartlett, and T. C. Ralph, “Measuring a photonic qubit without destroying it,” Phys. Rev. Lett. 92, 190402 (2004).
[CrossRef]

Beausoleil, R. G.

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302(R) (2005).

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]

Bergou, J. A.

Q. Lin, B. He, J. A. Bergou, and Y. H. Ren, “Processing multiphoton states through operation on a single photon: methods and applications,” Phys. Rev. A 80, 042311 (2009).

Beveratos, A.

J. A. W. van Houwelingen, N. Brunner, A. Beveratos, H. Zbinden, and N. Gisin, “Quantum teleportation with a three-Bell-state analyzer,” Phys. Rev. Lett. 96, 130502 (2006).
[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]

Brunner, N.

J. A. W. van Houwelingen, N. Brunner, A. Beveratos, H. Zbinden, and N. Gisin, “Quantum teleportation with a three-Bell-state analyzer,” Phys. Rev. Lett. 96, 130502 (2006).
[CrossRef]

Calsamiglia, J.

J. Calsamiglia, “Generalized measurements by linear elements,” Phys. Rev. A 65, 030301(R) (2002).
[CrossRef]

N. Lütkenhaus, J. Calsamiglia, and K. A. Suominen, “Bell measurements for teleportation,” Phys. Rev. A 59, 3295–3300 (1999).
[CrossRef]

Ceccarelli, R.

G. Vallone, R. Ceccarelli, F. De Martini, and P. Mataloni, “Hyperentanglement of two photons in three degrees of freedom,” Phys. Rev. A 79, 030301(R) (2009).
[CrossRef]

G. Vallone, R. Ceccarelli, F. De Martini, and P. Mataloni, “Hyperentanglement of two photons in three degrees of freedom,” Phys. Rev. A 79, 030301(R) (2009).
[CrossRef]

Chen, X. D.

X. M. Lin, Z. H. Chen, G. W. Lin, X. D. Chen, and B. B. Ni, “Optical Bell state and Greenberger-Horne-Zeilinger-state analyzers through the cavity input-output process,” Opt. Commun. 282, 3371–3374 (2009).
[CrossRef]

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P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowing, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007.
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D. M. Greenberger, M. A. Horne, and A. Zeilinger, in Bells Theorem, Quantum Theory, and Conceptions of the Universe, M. Kafatos, ed. (Kluwer, 1989).

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L. Xiao, C. Wang, W. Zhang, Y. D. Huang, J. D. Peng, and G. L. Long, “Efficient strategy for sharing entanglement via noisy channels with doubly entangled photon pairs,” Phys. Rev. A 77, 042315 (2008).
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J. S. Jin, C. S. Yu, and H. S. Song, “Nondestructive identification of the Bell diagonal state,” Phys. Rev. A 83, 032109 (2011).

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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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L. M. Duan and H. J. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. 92, 127902 (2004).
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H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, “Optimized phase switching using a single-atom nonlinearity,” J. Opt. B 5, 218 (2003).
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P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowing, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007.
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S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302(R) (2005).

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P. Kok, H. Lee, and J. P. Dowling, “Single-photon quantum-nondemolition detectors constructed with linear optics and projective measurements,” Phys. Rev. A 66, 063814 (2002).
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C. Wittmann, U. L. Andersen, M. Takeoka, D. Sych, and G. Leuchs, “Discrimination of binary coherent states using a homodyne detector and a photon number resolving detector,” Phys. Rev. A 81, 062338 (2010).
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X. H. Li, F. G. Deng, and H. Y. Zhou, “Improving the security of secure direct communication based on the secret transmitting order of particles,” Phys. Rev. A 74, 054302 (2006).

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C. Wang, Y. S. Li, and L. Hao, “Optical implementation of quantum random walks using weak cross-Kerr media,” Chin. Sci. Bull. 56, 2088–2091 (2011).
[CrossRef]

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X. M. Lin, Z. H. Chen, G. W. Lin, X. D. Chen, and B. B. Ni, “Optical Bell state and Greenberger-Horne-Zeilinger-state analyzers through the cavity input-output process,” Opt. Commun. 282, 3371–3374 (2009).
[CrossRef]

Lin, Q.

B. He, Q. Lin, and C. Simon, “Cross-Kerr nonlinearity between continuous-mode coherent states and single photons,” Phys. Rev. A 83, 053826 (2011).

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

Q. Lin, B. He, J. A. Bergou, and Y. H. Ren, “Processing multiphoton states through operation on a single photon: methods and applications,” Phys. Rev. A 80, 042311 (2009).

Lin, X. M.

X. M. Lin, Z. H. Chen, G. W. Lin, X. D. Chen, and B. B. Ni, “Optical Bell state and Greenberger-Horne-Zeilinger-state analyzers through the cavity input-output process,” Opt. Commun. 282, 3371–3374 (2009).
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R. Ursin, T. Jennewein, M. Aspelmeyer, R. Kaltenbaek, M. Lindenthal, P. Walther, and A. Zeilinger, “Communications: quantum teleportation across the Danube,” Nature 430, 849 (2004).
[CrossRef]

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

G. L. Long and X. S. Liu, “Theoretically efficient high-capacity quantum-key-distribution scheme,” Phys. Rev. A 65, 032302 (2002).
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Y. B. Sheng, F. G. Deng, and G. L. Long, “Multipartite electronic entanglement purification with charge detection,” Phys. Lett. A 375, 396–400 (2011).
[CrossRef]

Y. B. Sheng, F. G. Deng, and G. L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A 82, 032318 (2010).

C. Wang, L. Xiao, W. Y. Wang, G. Y. Zhang, and G. L. Long, “Quantum key distribution using polarization and frequency hyperentangled photons,” J. Opt. Soc. Am. B 26, 2072–2076 (2009).

L. Xiao, C. Wang, W. Zhang, Y. D. Huang, J. D. Peng, and G. L. Long, “Efficient strategy for sharing entanglement via noisy channels with doubly entangled photon pairs,” Phys. Rev. A 77, 042315 (2008).
[CrossRef]

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

F. G. Deng and G. L. Long, “Secure direct communication with a quantum one-time pad,” Phys. Rev. A 69, 052319 (2004).
[CrossRef]

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

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

Y. Xia, J. Song, P. M. Lu, and H. S. Song, “Effective quantum teleportation of an atomic state between two cavities with the cross-Kerr nonlinearity by interference of polarized photons,” J. Appl. Phys. 109, 103111 (2011).

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N. Lütkenhaus, J. Calsamiglia, and K. A. Suominen, “Bell measurements for teleportation,” Phys. Rev. A 59, 3295–3300 (1999).
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Z. J. Zhang and Z. X. Man, “Multiparty quantum secret sharing of classical messages based on entanglement swapping,” Phys. Rev. A 72, 022303 (2005).

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

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G. Vallone, R. Ceccarelli, F. De Martini, and P. Mataloni, “Hyperentanglement of two photons in three degrees of freedom,” Phys. Rev. A 79, 030301(R) (2009).
[CrossRef]

G. Vallone, R. Ceccarelli, F. De Martini, and P. Mataloni, “Hyperentanglement of two photons in three degrees of freedom,” Phys. Rev. A 79, 030301(R) (2009).
[CrossRef]

M. Barbieri, G. Vallone, P. Mataloni, and F. De Martini, “Complete and deterministic discrimination of polarization Bell states assisted by momentum entanglement,” Phys. Rev. A 75, 042317 (2007).
[CrossRef]

M. Barbieri, C. Cinelli, P. Mataloni, and F. De Martini, “Polarization-momentum hyperentangled states: realization and characterization,” Phys. Rev. A 72, 052110 (2005).
[CrossRef]

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X. B. 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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K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656–4659 (1996).
[CrossRef]

Milburn, G. J.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowing, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007.
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P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowing, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007.
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S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302(R) (2005).

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P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowing, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007.
[CrossRef]

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302(R) (2005).

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
[CrossRef]

Ni, B. B.

X. M. Lin, Z. H. Chen, G. W. Lin, X. D. Chen, and B. B. Ni, “Optical Bell state and Greenberger-Horne-Zeilinger-state analyzers through the cavity input-output process,” Opt. Commun. 282, 3371–3374 (2009).
[CrossRef]

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T. C. Ralph, S. D. Bartlett, J. L. O’Brien, G. J. Pryde, and H. M. Wiseman, “Quantum nondemolition measurements for quantum information,” Phys. Rev. A 73, 012113 (2006).

G. J. Pryde, J. L. O’Brien, A. G. White, T. C. Ralph, and H. M. Wiseman, “Measurement of quantum weak values of photon polarization,” Phys. Rev. Lett. 94, 220405 (2005).

G. J. Pryde, J. L. O’Brien, A. G. White, S. D. Bartlett, and T. C. Ralph, “Measuring a photonic qubit without destroying it,” Phys. Rev. Lett. 92, 190402 (2004).
[CrossRef]

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S. P. Walborn, S. Pádua, and C. H. Monken, “Hyperentanglement-assisted Bell-state analysis,” Phys. Rev. A 68, 042313 (2003).
[CrossRef]

Pahlke, K.

X. B. 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).

Peng, J. D.

L. Xiao, C. Wang, W. Zhang, Y. D. Huang, J. D. Peng, and G. L. Long, “Efficient strategy for sharing entanglement via noisy channels with doubly entangled photon pairs,” Phys. Rev. A 77, 042315 (2008).
[CrossRef]

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]

Peters, N. A.

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of hyperentangled photon pairs,” Phys. Rev. Lett. 95, 260501 (2005).
[CrossRef]

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T. C. Ralph, S. D. Bartlett, J. L. O’Brien, G. J. Pryde, and H. M. Wiseman, “Quantum nondemolition measurements for quantum information,” Phys. Rev. A 73, 012113 (2006).

G. J. Pryde, J. L. O’Brien, A. G. White, T. C. Ralph, and H. M. Wiseman, “Measurement of quantum weak values of photon polarization,” Phys. Rev. Lett. 94, 220405 (2005).

G. J. Pryde, J. L. O’Brien, A. G. White, S. D. Bartlett, and T. C. Ralph, “Measuring a photonic qubit without destroying it,” Phys. Rev. Lett. 92, 190402 (2004).
[CrossRef]

Ralph, T. C.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowing, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007.
[CrossRef]

T. C. Ralph, S. D. Bartlett, J. L. O’Brien, G. J. Pryde, and H. M. Wiseman, “Quantum nondemolition measurements for quantum information,” Phys. Rev. A 73, 012113 (2006).

G. J. Pryde, J. L. O’Brien, A. G. White, T. C. Ralph, and H. M. Wiseman, “Measurement of quantum weak values of photon polarization,” Phys. Rev. Lett. 94, 220405 (2005).

G. J. Pryde, J. L. O’Brien, A. G. White, S. D. Bartlett, and T. C. Ralph, “Measuring a photonic qubit without destroying it,” Phys. Rev. Lett. 92, 190402 (2004).
[CrossRef]

Razavi, M.

J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Physics 9, 16 (2007).
[CrossRef]

Ren, Y. H.

Q. Lin, B. He, J. A. Bergou, and Y. H. Ren, “Processing multiphoton states through operation on a single photon: methods and applications,” Phys. Rev. A 80, 042311 (2009).

Rigolin, G.

G. Gordon and G. Rigolin, “Generalized teleportation protocol,” Phys. Rev. A 73, 042309 (2006).

Rungta, P.

S. Ghose, N. Sinclair, S. Debnath, P. Rungta, and R. Stock, “Tripartite entanglement versus tripartite nonlocality in three-qubit Greenberger-Horne-Zeilinger-class states,” Phys. Rev. Lett. 102, 250404 (2009).
[CrossRef]

Sasaki, K.

H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, “Optimized phase switching using a single-atom nonlinearity,” J. Opt. B 5, 218 (2003).
[CrossRef]

Schuck, C.

C. Schuck, G. Huber, C. Kurtsiefer, and H. Weinfurter, “Complete deterministic linear optics Bell state analysis,” Phys. Rev. Lett. 96, 190501 (2006).
[CrossRef]

Shapiro, J. H.

J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Physics 9, 16 (2007).
[CrossRef]

J. H. Shapiro, “Single-photon Kerr nonlinearities do not help quantum computation,” Phys. Rev. A 73, 062305 (2006).

Sheng, Y. B.

Y. B. Sheng, F. G. Deng, and G. L. Long, “Multipartite electronic entanglement purification with charge detection,” Phys. Lett. A 375, 396–400 (2011).
[CrossRef]

Y. B. Sheng, F. G. Deng, and G. L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A 82, 032318 (2010).

Simon, C.

B. He, Q. Lin, and C. Simon, “Cross-Kerr nonlinearity between continuous-mode coherent states and single photons,” Phys. Rev. A 83, 053826 (2011).

Sinclair, N.

S. Ghose, N. Sinclair, S. Debnath, P. Rungta, and R. Stock, “Tripartite entanglement versus tripartite nonlocality in three-qubit Greenberger-Horne-Zeilinger-class states,” Phys. Rev. Lett. 102, 250404 (2009).
[CrossRef]

Song, H. S.

Y. Xia, J. Song, P. M. Lu, and H. S. Song, “Effective quantum teleportation of an atomic state between two cavities with the cross-Kerr nonlinearity by interference of polarized photons,” J. Appl. Phys. 109, 103111 (2011).

J. S. Jin, C. S. Yu, and H. S. Song, “Nondestructive identification of the Bell diagonal state,” Phys. Rev. A 83, 032109 (2011).

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).

Y. Xia and H. S. Song, “Controlled quantum secure direct communication using a non-symmetric quantum channel with quantum superdense coding,” Phys. Lett. A 364, 117–122 (2007).
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Song, J.

Y. Xia, J. Song, P. M. Lu, and H. S. Song, “Effective quantum teleportation of an atomic state between two cavities with the cross-Kerr nonlinearity by interference of polarized photons,” J. Appl. Phys. 109, 103111 (2011).

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).

Spiller, T. P.

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302(R) (2005).

Stock, R.

S. Ghose, N. Sinclair, S. Debnath, P. Rungta, and R. Stock, “Tripartite entanglement versus tripartite nonlocality in three-qubit Greenberger-Horne-Zeilinger-class states,” Phys. Rev. Lett. 102, 250404 (2009).
[CrossRef]

Suominen, K. A.

N. Lütkenhaus, J. Calsamiglia, and K. A. Suominen, “Bell measurements for teleportation,” Phys. Rev. A 59, 3295–3300 (1999).
[CrossRef]

Sych, D.

C. Wittmann, U. L. Andersen, M. Takeoka, D. Sych, and G. Leuchs, “Discrimination of binary coherent states using a homodyne detector and a photon number resolving detector,” Phys. Rev. A 81, 062338 (2010).
[CrossRef]

Takeoka, M.

C. Wittmann, U. L. Andersen, M. Takeoka, D. Sych, and G. Leuchs, “Discrimination of binary coherent states using a homodyne detector and a photon number resolving detector,” Phys. Rev. A 81, 062338 (2010).
[CrossRef]

Takeuchi, S.

H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, “Optimized phase switching using a single-atom nonlinearity,” J. Opt. B 5, 218 (2003).
[CrossRef]

Tsal, C. W.

C. W. Yang, C. W. Tsal, and T. Hwang, “Fault tolerant two-step quantum secure direct communication protocol against collective noises,” Sci. China-Phys. Mech. Astron. 54, 496–501 (2011).
[CrossRef]

Ursin, R.

R. Ursin, T. Jennewein, M. Aspelmeyer, R. Kaltenbaek, M. Lindenthal, P. Walther, and A. Zeilinger, “Communications: quantum teleportation across the Danube,” Nature 430, 849 (2004).
[CrossRef]

Vaidman, L.

L. Vaidman and N. Yoran, “Methods for reliable teleportation,” Phys. Rev. A 59, 116–125 (1999).
[CrossRef]

Vallone, G.

G. Vallone, R. Ceccarelli, F. De Martini, and P. Mataloni, “Hyperentanglement of two photons in three degrees of freedom,” Phys. Rev. A 79, 030301(R) (2009).
[CrossRef]

G. Vallone, R. Ceccarelli, F. De Martini, and P. Mataloni, “Hyperentanglement of two photons in three degrees of freedom,” Phys. Rev. A 79, 030301(R) (2009).
[CrossRef]

M. Barbieri, G. Vallone, P. Mataloni, and F. De Martini, “Complete and deterministic discrimination of polarization Bell states assisted by momentum entanglement,” Phys. Rev. A 75, 042317 (2007).
[CrossRef]

van Houwelingen, J. A. W.

J. A. W. van Houwelingen, N. Brunner, A. Beveratos, H. Zbinden, and N. Gisin, “Quantum teleportation with a three-Bell-state analyzer,” Phys. Rev. Lett. 96, 130502 (2006).
[CrossRef]

Walborn, S. P.

S. P. Walborn, S. Pádua, and C. H. Monken, “Hyperentanglement-assisted Bell-state analysis,” Phys. Rev. A 68, 042313 (2003).
[CrossRef]

Walther, P.

R. Ursin, T. Jennewein, M. Aspelmeyer, R. Kaltenbaek, M. Lindenthal, P. Walther, and A. Zeilinger, “Communications: quantum teleportation across the Danube,” Nature 430, 849 (2004).
[CrossRef]

Wang, C.

C. Wang, Y. S. Li, and L. Hao, “Optical implementation of quantum random walks using weak cross-Kerr media,” Chin. Sci. Bull. 56, 2088–2091 (2011).
[CrossRef]

C. Wang, L. Xiao, W. Y. Wang, G. Y. Zhang, and G. L. Long, “Quantum key distribution using polarization and frequency hyperentangled photons,” J. Opt. Soc. Am. B 26, 2072–2076 (2009).

L. Xiao, C. Wang, W. Zhang, Y. D. Huang, J. D. Peng, and G. L. Long, “Efficient strategy for sharing entanglement via noisy channels with doubly entangled photon pairs,” Phys. Rev. A 77, 042315 (2008).
[CrossRef]

Wang, W. Y.

Wei, T. C.

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
[CrossRef]

Weinfurter, H.

C. Schuck, G. Huber, C. Kurtsiefer, and H. Weinfurter, “Complete deterministic linear optics Bell state analysis,” Phys. Rev. Lett. 96, 190501 (2006).
[CrossRef]

P. G. Kwiat and H. Weinfurter, “Embedded Bell-state analysis,” Phys. Rev. A 58, R2623–R2626 (1998).
[CrossRef]

K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656–4659 (1996).
[CrossRef]

White, A. G.

G. J. Pryde, J. L. O’Brien, A. G. White, T. C. Ralph, and H. M. Wiseman, “Measurement of quantum weak values of photon polarization,” Phys. Rev. Lett. 94, 220405 (2005).

G. J. Pryde, J. L. O’Brien, A. G. White, S. D. Bartlett, and T. C. Ralph, “Measuring a photonic qubit without destroying it,” Phys. Rev. Lett. 92, 190402 (2004).
[CrossRef]

Wiseman, H. M.

T. C. Ralph, S. D. Bartlett, J. L. O’Brien, G. J. Pryde, and H. M. Wiseman, “Quantum nondemolition measurements for quantum information,” Phys. Rev. A 73, 012113 (2006).

G. J. Pryde, J. L. O’Brien, A. G. White, T. C. Ralph, and H. M. Wiseman, “Measurement of quantum weak values of photon polarization,” Phys. Rev. Lett. 94, 220405 (2005).

Wittmann, C.

C. Wittmann, U. L. Andersen, M. Takeoka, D. Sych, and G. Leuchs, “Discrimination of binary coherent states using a homodyne detector and a photon number resolving detector,” Phys. Rev. A 81, 062338 (2010).
[CrossRef]

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]

Xia, Y.

Y. Xia, J. Song, P. M. Lu, and H. S. Song, “Effective quantum teleportation of an atomic state between two cavities with the cross-Kerr nonlinearity by interference of polarized photons,” J. Appl. Phys. 109, 103111 (2011).

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).

Y. Xia and H. S. Song, “Controlled quantum secure direct communication using a non-symmetric quantum channel with quantum superdense coding,” Phys. Lett. A 364, 117–122 (2007).
[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).

Xiao, L.

C. Wang, L. Xiao, W. Y. Wang, G. Y. Zhang, and G. L. Long, “Quantum key distribution using polarization and frequency hyperentangled photons,” J. Opt. Soc. Am. B 26, 2072–2076 (2009).

L. Xiao, C. Wang, W. Zhang, Y. D. Huang, J. D. Peng, and G. L. Long, “Efficient strategy for sharing entanglement via noisy channels with doubly entangled photon pairs,” Phys. Rev. A 77, 042315 (2008).
[CrossRef]

Yang, C. W.

C. W. Yang, C. W. Tsal, and T. Hwang, “Fault tolerant two-step quantum secure direct communication protocol against collective noises,” Sci. China-Phys. Mech. Astron. 54, 496–501 (2011).
[CrossRef]

Yoran, N.

L. Vaidman and N. Yoran, “Methods for reliable teleportation,” Phys. Rev. A 59, 116–125 (1999).
[CrossRef]

Yu, C. S.

J. S. Jin, C. S. Yu, and H. S. Song, “Nondestructive identification of the Bell diagonal state,” Phys. Rev. A 83, 032109 (2011).

Zbinden, H.

J. A. W. van Houwelingen, N. Brunner, A. Beveratos, H. Zbinden, and N. Gisin, “Quantum teleportation with a three-Bell-state analyzer,” Phys. Rev. Lett. 96, 130502 (2006).
[CrossRef]

Zeilinger, A.

R. Ursin, T. Jennewein, M. Aspelmeyer, R. Kaltenbaek, M. Lindenthal, P. Walther, and A. Zeilinger, “Communications: quantum teleportation across the Danube,” Nature 430, 849 (2004).
[CrossRef]

K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656–4659 (1996).
[CrossRef]

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

Zhang, G. Y.

Zhang, S.

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).

Zhang, W.

L. Xiao, C. Wang, W. Zhang, Y. D. Huang, J. D. Peng, and G. L. Long, “Efficient strategy for sharing entanglement via noisy channels with doubly entangled photon pairs,” Phys. Rev. A 77, 042315 (2008).
[CrossRef]

Zhang, Z. J.

Z. J. Zhang and Z. X. Man, “Multiparty quantum secret sharing of classical messages based on entanglement swapping,” Phys. Rev. A 72, 022303 (2005).

Zhou, H. Y.

X. H. Li, F. G. Deng, and H. Y. Zhou, “Improving the security of secure direct communication based on the secret transmitting order of particles,” Phys. Rev. A 74, 054302 (2006).

Zhu, A. D.

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).

Zou, X. B.

X. B. 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).

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, 021127 (2008).

Chin. Sci. Bull. (1)

C. Wang, Y. S. Li, and L. Hao, “Optical implementation of quantum random walks using weak cross-Kerr media,” Chin. Sci. Bull. 56, 2088–2091 (2011).
[CrossRef]

J. Appl. Phys. (1)

Y. Xia, J. Song, P. M. Lu, and H. S. Song, “Effective quantum teleportation of an atomic state between two cavities with the cross-Kerr nonlinearity by interference of polarized photons,” J. Appl. Phys. 109, 103111 (2011).

J. Opt. B (1)

H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, “Optimized phase switching using a single-atom nonlinearity,” J. Opt. B 5, 218 (2003).
[CrossRef]

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

Nat. Phys. (1)

J. T. Barreiro, T. C. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
[CrossRef]

Nature (1)

R. Ursin, T. Jennewein, M. Aspelmeyer, R. Kaltenbaek, M. Lindenthal, P. Walther, and A. Zeilinger, “Communications: quantum teleportation across the Danube,” Nature 430, 849 (2004).
[CrossRef]

New J. Physics (1)

J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Physics 9, 16 (2007).
[CrossRef]

Opt. Commun. (1)

X. M. Lin, Z. H. Chen, G. W. Lin, X. D. Chen, and B. B. Ni, “Optical Bell state and Greenberger-Horne-Zeilinger-state analyzers through the cavity input-output process,” Opt. Commun. 282, 3371–3374 (2009).
[CrossRef]

Phys. Lett. A (2)

Y. B. Sheng, F. G. Deng, and G. L. Long, “Multipartite electronic entanglement purification with charge detection,” Phys. Lett. A 375, 396–400 (2011).
[CrossRef]

Y. Xia and H. S. Song, “Controlled quantum secure direct communication using a non-symmetric quantum channel with quantum superdense coding,” Phys. Lett. A 364, 117–122 (2007).
[CrossRef]

Phys. Rev. A (31)

X. H. Li, F. G. Deng, and H. Y. Zhou, “Improving the security of secure direct communication based on the secret transmitting order of particles,” Phys. Rev. A 74, 054302 (2006).

X. B. 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).

J. Gea-Banacloche, “Impossibility of large phase shifts via the giant Kerr effect with single-photon wave packets,” Phys. Rev. A 81, 043823 (2010).
[CrossRef]

B. He, Q. Lin, and C. Simon, “Cross-Kerr nonlinearity between continuous-mode coherent states and single photons,” Phys. Rev. A 83, 053826 (2011).

J. H. Shapiro, “Single-photon Kerr nonlinearities do not help quantum computation,” Phys. Rev. A 73, 062305 (2006).

Q. Lin, B. He, J. A. Bergou, and Y. H. Ren, “Processing multiphoton states through operation on a single photon: methods and applications,” Phys. Rev. A 80, 042311 (2009).

C. Wittmann, U. L. Andersen, M. Takeoka, D. Sych, and G. Leuchs, “Discrimination of binary coherent states using a homodyne detector and a photon number resolving detector,” Phys. Rev. A 81, 062338 (2010).
[CrossRef]

P. Kok, “Effects of self-phase-modulation on weak nonlinear optical quantum gates,” Phys. Rev. A 77, 013808 (2008).
[CrossRef]

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

T. C. Ralph, S. D. Bartlett, J. L. O’Brien, G. J. Pryde, and H. M. Wiseman, “Quantum nondemolition measurements for quantum information,” Phys. Rev. A 73, 012113 (2006).

J. S. Jin, C. S. Yu, and H. S. Song, “Nondestructive identification of the Bell diagonal state,” Phys. Rev. A 83, 032109 (2011).

P. Kok, H. Lee, and J. P. Dowling, “Single-photon quantum-nondemolition detectors constructed with linear optics and projective measurements,” Phys. Rev. A 66, 063814 (2002).
[CrossRef]

S. P. Walborn, S. Pádua, and C. H. Monken, “Hyperentanglement-assisted Bell-state analysis,” Phys. Rev. A 68, 042313 (2003).
[CrossRef]

M. Barbieri, G. Vallone, P. Mataloni, and F. De Martini, “Complete and deterministic discrimination of polarization Bell states assisted by momentum entanglement,” Phys. Rev. A 75, 042317 (2007).
[CrossRef]

Y. B. Sheng, F. G. Deng, and G. L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A 82, 032318 (2010).

S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302(R) (2005).

G. Vallone, R. Ceccarelli, F. De Martini, and P. Mataloni, “Hyperentanglement of two photons in three degrees of freedom,” Phys. Rev. A 79, 030301(R) (2009).
[CrossRef]

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

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

F. G. Deng and G. L. Long, “Secure direct communication with a quantum one-time pad,” Phys. Rev. A 69, 052319 (2004).
[CrossRef]

J. Calsamiglia, “Generalized measurements by linear elements,” Phys. Rev. A 65, 030301(R) (2002).
[CrossRef]

P. G. Kwiat and H. Weinfurter, “Embedded Bell-state analysis,” Phys. Rev. A 58, R2623–R2626 (1998).
[CrossRef]

L. Xiao, C. Wang, W. Zhang, Y. D. Huang, J. D. Peng, and G. L. Long, “Efficient strategy for sharing entanglement via noisy channels with doubly entangled photon pairs,” Phys. Rev. A 77, 042315 (2008).
[CrossRef]

M. Barbieri, C. Cinelli, P. Mataloni, and F. De Martini, “Polarization-momentum hyperentangled states: realization and characterization,” Phys. Rev. A 72, 052110 (2005).
[CrossRef]

G. Vallone, R. Ceccarelli, F. De Martini, and P. Mataloni, “Hyperentanglement of two photons in three degrees of freedom,” Phys. Rev. A 79, 030301(R) (2009).
[CrossRef]

G. Gordon and G. Rigolin, “Generalized teleportation protocol,” Phys. Rev. A 73, 042309 (2006).

Z. J. Zhang and Z. X. Man, “Multiparty quantum secret sharing of classical messages based on entanglement swapping,” Phys. Rev. A 72, 022303 (2005).

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).

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

L. Vaidman and N. Yoran, “Methods for reliable teleportation,” Phys. Rev. A 59, 116–125 (1999).
[CrossRef]

N. Lütkenhaus, J. Calsamiglia, and K. A. Suominen, “Bell measurements for teleportation,” Phys. Rev. A 59, 3295–3300 (1999).
[CrossRef]

Phys. Rev. Lett. (12)

K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656–4659 (1996).
[CrossRef]

J. A. W. van Houwelingen, N. Brunner, A. Beveratos, H. Zbinden, and N. Gisin, “Quantum teleportation with a three-Bell-state analyzer,” Phys. Rev. Lett. 96, 130502 (2006).
[CrossRef]

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

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

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of hyperentangled photon pairs,” Phys. Rev. Lett. 95, 260501 (2005).
[CrossRef]

S. Ghose, N. Sinclair, S. Debnath, P. Rungta, and R. Stock, “Tripartite entanglement versus tripartite nonlocality in three-qubit Greenberger-Horne-Zeilinger-class states,” Phys. Rev. Lett. 102, 250404 (2009).
[CrossRef]

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
[CrossRef]

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

C. Schuck, G. Huber, C. Kurtsiefer, and H. Weinfurter, “Complete deterministic linear optics Bell state analysis,” Phys. Rev. Lett. 96, 190501 (2006).
[CrossRef]

G. J. Pryde, J. L. O’Brien, A. G. White, T. C. Ralph, and H. M. Wiseman, “Measurement of quantum weak values of photon polarization,” Phys. Rev. Lett. 94, 220405 (2005).

G. J. Pryde, J. L. O’Brien, A. G. White, S. D. Bartlett, and T. C. Ralph, “Measuring a photonic qubit without destroying it,” Phys. Rev. Lett. 92, 190402 (2004).
[CrossRef]

L. M. Duan and H. J. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. 92, 127902 (2004).
[CrossRef]

Rev. Mod. Phys. (1)

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowing, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007.
[CrossRef]

Sci. China-Phys. Mech. Astron. (1)

C. W. Yang, C. W. Tsal, and T. Hwang, “Fault tolerant two-step quantum secure direct communication protocol against collective noises,” Sci. China-Phys. Mech. Astron. 54, 496–501 (2011).
[CrossRef]

Other (1)

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

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Figures (8)

Fig. 1.
Fig. 1.

Schematic diagram of the present HGSA scheme for spatial-mode entangled three-photon GHZ states. The QND is used to distinguish the four groups of GHZ states |Ψ1±s, |Ψ2±s, |Ψ3±s, and |Ψ4±s.

Fig. 2.
Fig. 2.

The setup for distinguishing the relative phases of the GHZ states in spatial modes. BSs denote the 5050 beamsplitters, act as the Hadamard operations. θi (i=1, 2, 3, 4, 5, 6) represent six different cross-Kerr nonlinear media with the phase shift θi. If the three photons appear at the outports d1d3d5, d1d4d6, d2d3d6, or d2d4d5, then, the three photons are originally in one of the four GHZ states |Ψy+s; if the three photons appear at the outports d1d3d6, d1d4d5, d2d3d5, or d2d4d6, the three photons are originally in one of the four GHZ states |Ψys (y={1,2,3,4}).

Fig. 3.
Fig. 3.

Experimental setup for the HGSA scheme for GHZ states in polarization. PBSs denote the polarization beam splitters. This QND is used to distinguish the four groups of GHZ states |Ψ1±p, |Ψ2±p, |Ψ3±p, and |Ψ4±p.

Fig. 4.
Fig. 4.

The setup for distinguishing the relative phases of the GHZ states in polarization. PBSs denote the polarization beam splitters. The R45s denote the wave plates which can rotate the horizontal and vertical polarizations by 45°, just like a Hadamard operation on the polarization. Dj (j=1, 2, 3, 4, 5, 6) are detectors. If the three photons click the detectors at the outports D1D3D5, D1D4D6, D2D3D6, or D2D4D5, then, the three photons are originally in one of the four GHZ states |Ψy+p; if the three photons click the detectors at the outports D1D3D6, D1D4D5, D2D3D5, or D2D4D6, then, the three photons are originally in one of the four GHZ states |Ψyp. (y={1,2,3,4})

Fig. 5.
Fig. 5.

Schematic diagram of the present HGSA scheme for spatial-mode entangled N-photon GHZ states.

Fig. 6.
Fig. 6.

The setup for distinguishing the two GHZ states in each group |Ψν±s, ν{1,2,,2N1}.

Fig. 7.
Fig. 7.

Experimental setup for the HGSA scheme for N-photon GHZ states in polarization.

Fig. 8.
Fig. 8.

The setup for distinguishing the two N-photon GHZ states in polarization in each group |Ψν±p, ν{1,2,,2N1}.

Tables (2)

Tables Icon

Table 1. Corresponding Relations Between |Ψy±s (y={1,2,3,4}) and |α1|α2’s Phase Shift

Tables Icon

Table 2. Corresponding Relations Between |Ψy±P (y={1,2,3,4}) and |α1|α2’s Phase Shift

Equations (41)

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

Uck|φ|α=eiHQNDt/(a|0+b|1)|α=a|0|α+b|1|αeiθ.
|ζ1+PS=12(|HHH+|VVV)abc(|a1b1c1+|a2b2c2)abc,
|Ψ1±p=12(|HHH±|VVV),
|Ψ2±p=12(|VHH±|HVV),
|Ψ3±p=12(|HVH±|VHV),
|Ψ4±p=12(|HHV±|VVH),
|Ψ1±s=12(|a1b1c1±|a2b2c2),
|Ψ2±s=12(|a2b1c1±|a1b2c2),
|Ψ3±s=12(|a1b2c1±|a2b1c2),
|Ψ4±s=12(|a1b1c2±|a2b2c1).
|Ψ1±s|α1|α2=12(|a1b1c1±|a2b2c2)|α1|α212(|a1b1c1|αeiθ11|αeiθ22±|a2b2c2|αeiθ11|αeiθ2),
|Ψ2±s|α1|α2=12(|a2b1c1±|a1b2c2)|α1|α212(|a2b1c1|α1|α2±|a1b2c2|α1|α2)=|Ψ2±s|α1|α2,
|Ψ3±s|α1|α2=12(|a1b2c1±|a2b1c2)|α1|α212(|a1b2c1|α1|αeiθ22±|a2b1c2|α1|αeiθ22),
|Ψ4±s|α1|α2=12(|a1b1c2±|a2b2c1)|α1|α212(|a1b1c2|αeiθ11|α2±|a2b2c1|αeiθ11|α2).
Ka1(b1,c1)+12(Kd1(3,5)++Kd2(4,6)+),
Ka2(b2,c2)+12(Kd1(3,5)+Kd2(4,6)+).
|Ψ1+s=12(d1d3d5+d1d4d6+d2d3d6+d2d4d5),
|Ψ1s=12(d1d3d6+d1d4d5+d2d3d5+d2d4d6),
|Ψ2+s=12(d1d3d5+d1d4d6d2d3d6d2d4d5),
|Ψ2s=12(d1d3d6+d1d4d6d2d3d5d2d4d6),
|Ψ3+s=12(d1d3d5d1d4d6+d2d3d6d2d4d5),
|Ψ3s=12(d1d3d6d1d4d5+d2d3d5d2d4d6),
|Ψ4+s=12(d1d3d5d1d4d6d2d3d6+d2d4d5),
|Ψ4s=12(d1d3d6+d1d4d5+d2d3d5d2d4d6).
|Ψ1±P|α1|α2=12(|HHH±|VVV)|α1|α212(|HHH|αeiθ11|αeiθ22±|VVV|αeiθ11|αeiθ22),
|Ψ2±P|α1|α2=12(|VHH±|HVV)|α1|α212(|VHH|α1|α2±|HVV|α1|α2)=|Ψ2±P|α1|α2,
|Ψ3±P|α1|α2=12(|HVH±|VHV)|α1|α212(|HVH|α1|αeiθ22±|VHV|α1|αeiθ22),
|Ψ4±P|α1|α2=12(|HHV±|VVH)|α1|α212(|HHV|αeiθ11|α2±|VVH|αeiθ11|α2).
|H12(|H+|V),
|V12(|H|V).
|Ψ1+p=12(D1D3D5+D1D4D6+D2D3D6+D2D4D5),
|Ψ1p=12(D1D3D6+D1D4D5+D2D3D5+D2D4D6),
|Ψ2+p=12(D1D3D5+D1D4D6D2D3D6D2D4D5),
|Ψ2p=12(D1D3D6+D1D4D6D2D3D5D2D4D6),
|Ψ3+p=12(D1D3D5D1D4D6+D2D3D6D2D4D5),
|Ψ3p=12(D1D3D6D1D4D5+D2D3D5D2D4D6),
|Ψ4+p=12(D1D3D5D1D4D6D2D3D6+D2D4D5),
|Ψ4p=12(D1D3D6+D1D4D5+D2D3D5D2D4D6).
|ϖi=12(|HHH+|VVV)SiHiTi(|a1b1c1+|a2b2c2)SiHiTi,
|ϖi=12(|HHV|VVH)SiHiTi(|a1b1c2|a2b2c1)SiHiTi.
|ϖi=12(|HHV|VVH)SiHiTi(|a1b1c2|a2b2c1)SiHiTi=|Ψ4p|Ψ4s.

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