Abstract

We propose two schemes for concentration of hyperentanglement of nonlocal multipartite states which are simultaneously entangled in the polarization and spatial modes. One scheme uses an auxiliary single-photon state prepared according to the parameters of the less-entangled states. The other scheme uses two less-entangled states with unknown parameters to distill the maximal hyperentanglement. The procrustean concentration is realized by two parity check measurements in both the two degrees of freedom. Nondestructive quantum nondemolition detectors based on cross-Kerr nonlinearity are used to implement the parity check, which makes the unsuccessful instances reusable in the next concentration round. The success probabilities in both schemes can be made to approach unity by iteration. Moreover, in both schemes only one of the N parties has to perform the parity check measurements. Our schemes are efficient and useful for quantum information processing involving hyperentanglement.

© 2015 Optical Society of America

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Single-photon-assisted entanglement concentration of a multiphoton system in a partially entangled W state with weak cross-Kerr nonlinearity

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    [Crossref]
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    [Crossref] [PubMed]
  32. Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics,” Phys. Rev. A 77, 062325 (2008).
    [Crossref]
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    [Crossref]
  34. X. H. Li, “Deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044304 (2010).
    [Crossref]
  35. Y. B. Sheng and F. G. Deng, “One-step deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044305 (2010).
    [Crossref]
  36. F. G. Deng, “One-step error correction for multipartite polarization entanglement,” Phys. Rev. A 83, 062316 (2011).
    [Crossref]
  37. P. G. Kwiat and H. Weinfurter, “Embedded Bell-state analysis,” Phys. Rev. A 58, R2623–R2626 (1998).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  45. X. H. Li, X. Chen, and Z. Zeng, “Hyperconcentration for entanglement in two degrees of freedom,” J. Opt. Soc. Am. B 30, 2774–2780 (2013).
    [Crossref]
  46. X. Chen, Z. Zeng, and X. H. Li, “Hyperconcentration based on projection measurements,” Commun. Theor. Phys. 61, 322–328 (2014).
    [Crossref]
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    [Crossref]
  48. B. C. Ren and G. L. Long, “General hyperentanglement concentration for photon systems assisted by quantum-dot spins inside optical microcavities,” Opt. Express 22, 6547–6561 (2014).
    [Crossref] [PubMed]
  49. K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004).
    [Crossref]
  50. P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowing, and G. J. Milbum, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007)
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  55. E. Waks and J. Vuckovic, “Dipole induced transparency in drop-filter cavity-waveguide systems,” Phys. Rev. Lett. 96, 153601 (2006).
    [Crossref] [PubMed]
  56. 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] [PubMed]
  57. C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat, D. P. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett. 104, 160503 (2010).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]

2014 (5)

B. C. Ren and F. G. Deng, “Hyper-parallel photonic quantum computation with coupled quantum dots,” Sci. Rep. 4, 4623 (2014).
[Crossref] [PubMed]

X. H. Li and S. Ghose, “Hyperconcentration for multipartite entanglement via linear optics,” Laser phys. Lett. 11, 125201 (2014).
[Crossref]

T. J. Wang, C. Cao, and C. Wang, “Linear-optical implementation of hyperdistillation from photon loss,” Phys. Rev. A 89, 052303 (2014).
[Crossref]

X. Chen, Z. Zeng, and X. H. Li, “Hyperconcentration based on projection measurements,” Commun. Theor. Phys. 61, 322–328 (2014).
[Crossref]

B. C. Ren and G. L. Long, “General hyperentanglement concentration for photon systems assisted by quantum-dot spins inside optical microcavities,” Opt. Express 22, 6547–6561 (2014).
[Crossref] [PubMed]

2013 (6)

X. H. Li, X. Chen, and Z. Zeng, “Hyperconcentration for entanglement in two degrees of freedom,” J. Opt. Soc. Am. B 30, 2774–2780 (2013).
[Crossref]

B. C. Ren and F. G. Deng, “Hyperentanglement purification and concentration assisted by diamond NV centers inside photonic crystal cavities,” Laser Phys. Lett. 10, 115201 (2013).
[Crossref]

S. Song, Y. Cao, Y. B. Sheng, and G. L. Long, “Complete Greenberger-Horne-Zeilinger state analyzer using hyperentanglement,” Quantum Inf. Process. 12, 381–393 (2013).
[Crossref]

B. C. Ren, F. F. Du, and F. G. Deng, “Hyperentanglement concentration for two-photon four-qubit systems with linear optics”, Phys. Rev. A 88, 012302 (2013).
[Crossref]

B. C. Ren, H. R. Wei, and F. G. Deng, “Deterministic photonic spatial-polarization hyper-controlled-not gate assisted by a quantum dot inside a one-side optical microcavity,” Laser phys. Lett. 10, 095202 (2013).
[Crossref]

Y. B. Sheng and L. Zhou, “Quantum entanglement concentration based on nonlinear optics for quantum communications,” Entropy 15, 1776–1820 (2013).
[Crossref]

2012 (4)

Y. B. Sheng, L. Zhou, and S. M. Zhao, “Efficient two-step entanglement concentration for arbitrary W states,” Phys. Rev. A 85, 042302 (2012).
[Crossref]

F. G. Deng, “Optimal nonlocal multipartite entanglement concentration based on projection measurements,” Phys. Rev. A 85, 022311 (2012).
[Crossref]

Y. B. Sheng, L. Zhou, S. M. Zhao, and B. Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A 85, 012307 (2012).
[Crossref]

B. Gu, “Single-photon-assisted entanglement concentration of partially entangled multiphoton W states with linear optics,” J. Opt. Soc. Am. B 29, 1685–1689 (2012).
[Crossref]

2011 (7)

C. Zhu and G. Huang, “Giant kerr nonlinearity, controlled entangled photons and polarization phase gates in coupled quantum-well structures,” Opt. Express 19, 23364–23376 (2011).
[Crossref] [PubMed]

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

A. Feizpour, X. Xing, and A. M. Steinberg, “Amplifying single-photon nonlinearity using weak measurements,” Phys. Rev. Lett. 107, 133603 (2011).
[Crossref] [PubMed]

A. V. Gorshkov, J. Otterbach, M. Fleischhauer, T. Pohl, and M. D. Lukin, “Photon-photon interactions via Rydberg blockade,” Phys. Rev. Lett. 107, 133602 (2011).
[Crossref] [PubMed]

E. Shahmoon, G. Kurizki, M. Fleischhauer, and D. Petrosyan, “Strongly interacting photons in hollow-core waveguides,” Phys. Rev. A 83, 033806 (2011).
[Crossref]

C. Wang, Y. Zhan, and G. S. Jin, “Polarization-entanglement purification and concentration using cross-Kerr nonlinearity,” Quantum Inform. Comput. 11, 988–1002 (2011).

F. G. Deng, “One-step error correction for multipartite polarization entanglement,” Phys. Rev. A 83, 062316 (2011).
[Crossref]

2010 (6)

Y. B. Sheng and F. G. Deng, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A 81, 032307 (2010).
[Crossref]

X. H. Li, “Deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044304 (2010).
[Crossref]

Y. B. Sheng and F. G. Deng, “One-step deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044305 (2010).
[Crossref]

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Single-photon entanglement concentration for long-distance quantum communication,” Quantum Inform. Comput. 10, 0272 (2010).

A. Yildiz, “Optimal distillation of three-qubit W states,” Phys. Rev. A 82, 012317 (2010).
[Crossref]

C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat, D. P. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett. 104, 160503 (2010).
[Crossref] [PubMed]

2009 (1)

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

2008 (3)

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]

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics,” Phys. Rev. A 77, 062325 (2008).
[Crossref]

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics,” Phys. Rev. A 77, 062325 (2008).
[Crossref]

2007 (2)

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]

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

2006 (3)

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

E. Waks and J. Vuckovic, “Dipole induced transparency in drop-filter cavity-waveguide systems,” Phys. Rev. Lett. 96, 153601 (2006).
[Crossref] [PubMed]

S. P. Walborn, M. P. Almeida, P. H. SoutoRibeiro, and C. H. Monken, “Quantum information processing with hyperentangled photon states,” Quantum Inform. Comput. 6, 336–350 (2006).

2005 (3)

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]

C. Wang, F. G. Deng, Y. S. Li, X. S. Liu, and G. L. Long, “Quantum secure direct communication with highdimension quantum superdense coding,” Phys. Rev. A 71, 044305 (2005).
[Crossref]

X. F. Ren, G. P. Guo, and G. C. Guo, “Complete Bell-states analysis using hyper-entanglement,” Physics Letters A 343, 8–11 (2005).
[Crossref]

2004 (2)

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

2003 (3)

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

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

2002 (2)

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

C. Simon and J. W. Pan, “Polarization entanglement purification using spatial entanglement,” Phys. Rev. Lett. 89, 257901 (2002).
[Crossref] [PubMed]

2001 (2)

T. Yamamoto, M. Koashi, and N. Imoto, “Concentration and purification scheme for two partially entangled photon pairs,” Phys. Rev. A 64, 012304 (2001).
[Crossref]

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

2000 (1)

B. S. Shi, Y. K. Jiang, and G. C. Guo, “Optimal entanglement purification via entanglement swapping,” Phys. Rev. A 62, 054301 (2000).
[Crossref]

1999 (1)

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

1998 (2)

H. J. Briege, W. Dür, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932–5935 (1998).
[Crossref]

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

1997 (1)

P. G. Kwiat, “Hyper-entangled states,” J. Mod. Opt,  44, 2173–2184 (1997).
[Crossref]

1996 (1)

C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046–2052 (1996).
[Crossref] [PubMed]

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 (2)

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

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bells theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
[Crossref] [PubMed]

1991 (1)

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

Almeida, M. P.

S. P. Walborn, M. P. Almeida, P. H. SoutoRibeiro, and C. H. Monken, “Quantum information processing with hyperentangled photon states,” Quantum Inform. Comput. 6, 336–350 (2006).

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]

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]

Bartlett, S. D.

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] [PubMed]

Bennett, C. H.

C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046–2052 (1996).
[Crossref] [PubMed]

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

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bells theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
[Crossref] [PubMed]

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

Bernstein, H. J.

C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046–2052 (1996).
[Crossref] [PubMed]

Bonato, C.

C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat, D. P. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett. 104, 160503 (2010).
[Crossref] [PubMed]

Bose, S.

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

Bouwmeester, D.

C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat, D. P. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett. 104, 160503 (2010).
[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]

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bells theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
[Crossref] [PubMed]

Briege, H. J.

H. J. Briege, W. Dür, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932–5935 (1998).
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Cao, C.

T. J. Wang, C. Cao, and C. Wang, “Linear-optical implementation of hyperdistillation from photon loss,” Phys. Rev. A 89, 052303 (2014).
[Crossref]

Cao, Y.

S. Song, Y. Cao, Y. B. Sheng, and G. L. Long, “Complete Greenberger-Horne-Zeilinger state analyzer using hyperentanglement,” Quantum Inf. Process. 12, 381–393 (2013).
[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 (2009)
[Crossref]

Chen, X.

X. Chen, Z. Zeng, and X. H. Li, “Hyperconcentration based on projection measurements,” Commun. Theor. Phys. 61, 322–328 (2014).
[Crossref]

X. H. Li, X. Chen, and Z. Zeng, “Hyperconcentration for entanglement in two degrees of freedom,” J. Opt. Soc. Am. B 30, 2774–2780 (2013).
[Crossref]

Cirac, J. I.

H. J. Briege, W. Dür, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932–5935 (1998).
[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]

De Martini, F.

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).
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De. Martini, F.

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

B. C. Ren and F. G. Deng, “Hyper-parallel photonic quantum computation with coupled quantum dots,” Sci. Rep. 4, 4623 (2014).
[Crossref] [PubMed]

B. C. Ren, H. R. Wei, and F. G. Deng, “Deterministic photonic spatial-polarization hyper-controlled-not gate assisted by a quantum dot inside a one-side optical microcavity,” Laser phys. Lett. 10, 095202 (2013).
[Crossref]

B. C. Ren, F. F. Du, and F. G. Deng, “Hyperentanglement concentration for two-photon four-qubit systems with linear optics”, Phys. Rev. A 88, 012302 (2013).
[Crossref]

B. C. Ren and F. G. Deng, “Hyperentanglement purification and concentration assisted by diamond NV centers inside photonic crystal cavities,” Laser Phys. Lett. 10, 115201 (2013).
[Crossref]

F. G. Deng, “Optimal nonlocal multipartite entanglement concentration based on projection measurements,” Phys. Rev. A 85, 022311 (2012).
[Crossref]

F. G. Deng, “One-step error correction for multipartite polarization entanglement,” Phys. Rev. A 83, 062316 (2011).
[Crossref]

Y. B. Sheng and F. G. Deng, “One-step deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044305 (2010).
[Crossref]

Y. B. Sheng and F. G. Deng, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A 81, 032307 (2010).
[Crossref]

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Single-photon entanglement concentration for long-distance quantum communication,” Quantum Inform. Comput. 10, 0272 (2010).

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics,” Phys. Rev. A 77, 062325 (2008).
[Crossref]

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics,” Phys. Rev. A 77, 062325 (2008).
[Crossref]

C. Wang, F. G. Deng, Y. S. Li, X. S. Liu, and G. L. Long, “Quantum secure direct communication with highdimension quantum superdense coding,” Phys. Rev. A 71, 044305 (2005).
[Crossref]

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

Ding, D. P.

C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat, D. P. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett. 104, 160503 (2010).
[Crossref] [PubMed]

Dowing, J. P.

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

Du, F. F.

B. C. Ren, F. F. Du, and F. G. Deng, “Hyperentanglement concentration for two-photon four-qubit systems with linear optics”, Phys. Rev. A 88, 012302 (2013).
[Crossref]

Dür, W.

H. J. Briege, W. Dür, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932–5935 (1998).
[Crossref]

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A. K. Ekert, “Quantum cryptography based on Bells theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
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A. Feizpour, X. Xing, and A. M. Steinberg, “Amplifying single-photon nonlinearity using weak measurements,” Phys. Rev. Lett. 107, 133603 (2011).
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Fleischhauer, M.

A. V. Gorshkov, J. Otterbach, M. Fleischhauer, T. Pohl, and M. D. Lukin, “Photon-photon interactions via Rydberg blockade,” Phys. Rev. Lett. 107, 133602 (2011).
[Crossref] [PubMed]

E. Shahmoon, G. Kurizki, M. Fleischhauer, and D. Petrosyan, “Strongly interacting photons in hollow-core waveguides,” Phys. Rev. A 83, 033806 (2011).
[Crossref]

Ghose, S.

X. H. Li and S. Ghose, “Hyperconcentration for multipartite entanglement via linear optics,” Laser phys. Lett. 11, 125201 (2014).
[Crossref]

Gorshkov, A. V.

A. V. Gorshkov, J. Otterbach, M. Fleischhauer, T. Pohl, and M. D. Lukin, “Photon-photon interactions via Rydberg blockade,” Phys. Rev. Lett. 107, 133602 (2011).
[Crossref] [PubMed]

Gu, B.

Gudat, J.

C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat, D. P. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett. 104, 160503 (2010).
[Crossref] [PubMed]

Guo, G. C.

X. F. Ren, G. P. Guo, and G. C. Guo, “Complete Bell-states analysis using hyper-entanglement,” Physics Letters A 343, 8–11 (2005).
[Crossref]

B. S. Shi, Y. K. Jiang, and G. C. Guo, “Optimal entanglement purification via entanglement swapping,” Phys. Rev. A 62, 054301 (2000).
[Crossref]

Guo, G. P.

X. F. Ren, G. P. Guo, and G. C. Guo, “Complete Bell-states analysis using hyper-entanglement,” Physics Letters A 343, 8–11 (2005).
[Crossref]

Haupt, F.

C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat, D. P. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett. 104, 160503 (2010).
[Crossref] [PubMed]

He, B.

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

Huang, G.

Huber, G.

C. Schuck, G. Huber, C. Kurtsiefer, and H. Weinfurter, “Complete deterministic linear optics bell state analysis,” Phys. Rev. Lett. 96, 190501 (2006).
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Imoto, N.

T. Yamamoto, M. Koashi, and N. Imoto, “Concentration and purification scheme for two partially entangled photon pairs,” Phys. Rev. A 64, 012304 (2001).
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Jiang, Y. K.

B. S. Shi, Y. K. Jiang, and G. C. Guo, “Optimal entanglement purification via entanglement swapping,” Phys. Rev. A 62, 054301 (2000).
[Crossref]

Jin, G. S.

C. Wang, Y. Zhan, and G. S. Jin, “Polarization-entanglement purification and concentration using cross-Kerr nonlinearity,” Quantum Inform. Comput. 11, 988–1002 (2011).

Jozsa, R.

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

Knight, P. L.

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

Koashi, M.

T. Yamamoto, M. Koashi, and N. Imoto, “Concentration and purification scheme for two partially entangled photon pairs,” Phys. Rev. A 64, 012304 (2001).
[Crossref]

Kok, P.

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

Kurizki, G.

E. Shahmoon, G. Kurizki, M. Fleischhauer, and D. Petrosyan, “Strongly interacting photons in hollow-core waveguides,” Phys. Rev. A 83, 033806 (2011).
[Crossref]

Kurtsiefer, C.

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

Kwiat, P. G.

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).
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J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of hyperentangled photon pairs,” Phys. Rev. Lett. 95, 260501 (2005).
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P. G. Kwiat and H. Weinfurter, “Embedded Bell-state analysis,” Phys. Rev. A 58, R2623–R2626 (1998).
[Crossref]

P. G. Kwiat, “Hyper-entangled states,” J. Mod. Opt,  44, 2173–2184 (1997).
[Crossref]

Langford, N. K.

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]

Li, X. H.

X. H. Li and S. Ghose, “Hyperconcentration for multipartite entanglement via linear optics,” Laser phys. Lett. 11, 125201 (2014).
[Crossref]

X. Chen, Z. Zeng, and X. H. Li, “Hyperconcentration based on projection measurements,” Commun. Theor. Phys. 61, 322–328 (2014).
[Crossref]

X. H. Li, X. Chen, and Z. Zeng, “Hyperconcentration for entanglement in two degrees of freedom,” J. Opt. Soc. Am. B 30, 2774–2780 (2013).
[Crossref]

X. H. Li, “Deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044304 (2010).
[Crossref]

Li, Y. S.

C. Wang, F. G. Deng, Y. S. Li, X. S. Liu, and G. L. Long, “Quantum secure direct communication with highdimension quantum superdense coding,” Phys. Rev. A 71, 044305 (2005).
[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).
[Crossref]

Liu, X. S.

C. Wang, F. G. Deng, Y. S. Li, X. S. Liu, and G. L. Long, “Quantum secure direct communication with highdimension quantum superdense coding,” Phys. Rev. A 71, 044305 (2005).
[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).
[Crossref]

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

Long, G. L.

B. C. Ren and G. L. Long, “General hyperentanglement concentration for photon systems assisted by quantum-dot spins inside optical microcavities,” Opt. Express 22, 6547–6561 (2014).
[Crossref] [PubMed]

S. Song, Y. Cao, Y. B. Sheng, and G. L. Long, “Complete Greenberger-Horne-Zeilinger state analyzer using hyperentanglement,” Quantum Inf. Process. 12, 381–393 (2013).
[Crossref]

C. Wang, F. G. Deng, Y. S. Li, X. S. Liu, and G. L. Long, “Quantum secure direct communication with highdimension quantum superdense coding,” Phys. Rev. A 71, 044305 (2005).
[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).
[Crossref]

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

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

Lukin, M. D.

A. V. Gorshkov, J. Otterbach, M. Fleischhauer, T. Pohl, and M. D. Lukin, “Photon-photon interactions via Rydberg blockade,” Phys. Rev. Lett. 107, 133602 (2011).
[Crossref] [PubMed]

Mataloni, P.

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

Mermin, N. D.

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bells theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
[Crossref] [PubMed]

Milbum, G. J.

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

Monken, C. H.

S. P. Walborn, M. P. Almeida, P. H. SoutoRibeiro, and C. H. Monken, “Quantum information processing with hyperentangled photon states,” Quantum Inform. Comput. 6, 336–350 (2006).

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

Munro, W. J.

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

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

Nemoto, K.

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

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

O’Brien, J. L.

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] [PubMed]

Oemrawsingh, S. S. R.

C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat, D. P. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett. 104, 160503 (2010).
[Crossref] [PubMed]

Otterbach, J.

A. V. Gorshkov, J. Otterbach, M. Fleischhauer, T. Pohl, and M. D. Lukin, “Photon-photon interactions via Rydberg blockade,” Phys. Rev. Lett. 107, 133602 (2011).
[Crossref] [PubMed]

Pádua, S.

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

Pan, J. W.

C. Simon and J. W. Pan, “Polarization entanglement purification using spatial entanglement,” Phys. Rev. Lett. 89, 257901 (2002).
[Crossref] [PubMed]

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

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]

Petrosyan, D.

E. Shahmoon, G. Kurizki, M. Fleischhauer, and D. Petrosyan, “Strongly interacting photons in hollow-core waveguides,” Phys. Rev. A 83, 033806 (2011).
[Crossref]

Pohl, T.

A. V. Gorshkov, J. Otterbach, M. Fleischhauer, T. Pohl, and M. D. Lukin, “Photon-photon interactions via Rydberg blockade,” Phys. Rev. Lett. 107, 133602 (2011).
[Crossref] [PubMed]

Popescu, S.

C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046–2052 (1996).
[Crossref] [PubMed]

Pryde, G. J.

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] [PubMed]

Ralph, T. C.

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

Ren, B. C.

B. C. Ren and G. L. Long, “General hyperentanglement concentration for photon systems assisted by quantum-dot spins inside optical microcavities,” Opt. Express 22, 6547–6561 (2014).
[Crossref] [PubMed]

B. C. Ren and F. G. Deng, “Hyper-parallel photonic quantum computation with coupled quantum dots,” Sci. Rep. 4, 4623 (2014).
[Crossref] [PubMed]

B. C. Ren, H. R. Wei, and F. G. Deng, “Deterministic photonic spatial-polarization hyper-controlled-not gate assisted by a quantum dot inside a one-side optical microcavity,” Laser phys. Lett. 10, 095202 (2013).
[Crossref]

B. C. Ren, F. F. Du, and F. G. Deng, “Hyperentanglement concentration for two-photon four-qubit systems with linear optics”, Phys. Rev. A 88, 012302 (2013).
[Crossref]

B. C. Ren and F. G. Deng, “Hyperentanglement purification and concentration assisted by diamond NV centers inside photonic crystal cavities,” Laser Phys. Lett. 10, 115201 (2013).
[Crossref]

Ren, X. F.

X. F. Ren, G. P. Guo, and G. C. Guo, “Complete Bell-states analysis using hyper-entanglement,” Physics Letters A 343, 8–11 (2005).
[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] [PubMed]

Schumacher, B.

C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046–2052 (1996).
[Crossref] [PubMed]

Shahmoon, E.

E. Shahmoon, G. Kurizki, M. Fleischhauer, and D. Petrosyan, “Strongly interacting photons in hollow-core waveguides,” Phys. Rev. A 83, 033806 (2011).
[Crossref]

Sheng, Y. B.

Y. B. Sheng and L. Zhou, “Quantum entanglement concentration based on nonlinear optics for quantum communications,” Entropy 15, 1776–1820 (2013).
[Crossref]

S. Song, Y. Cao, Y. B. Sheng, and G. L. Long, “Complete Greenberger-Horne-Zeilinger state analyzer using hyperentanglement,” Quantum Inf. Process. 12, 381–393 (2013).
[Crossref]

Y. B. Sheng, L. Zhou, and S. M. Zhao, “Efficient two-step entanglement concentration for arbitrary W states,” Phys. Rev. A 85, 042302 (2012).
[Crossref]

Y. B. Sheng, L. Zhou, S. M. Zhao, and B. Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A 85, 012307 (2012).
[Crossref]

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Single-photon entanglement concentration for long-distance quantum communication,” Quantum Inform. Comput. 10, 0272 (2010).

Y. B. Sheng and F. G. Deng, “One-step deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044305 (2010).
[Crossref]

Y. B. Sheng and F. G. Deng, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A 81, 032307 (2010).
[Crossref]

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics,” Phys. Rev. A 77, 062325 (2008).
[Crossref]

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics,” Phys. Rev. A 77, 062325 (2008).
[Crossref]

Shi, B. S.

B. S. Shi, Y. K. Jiang, and G. C. Guo, “Optimal entanglement purification via entanglement swapping,” Phys. Rev. A 62, 054301 (2000).
[Crossref]

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).
[Crossref]

C. Simon and J. W. Pan, “Polarization entanglement purification using spatial entanglement,” Phys. Rev. Lett. 89, 257901 (2002).
[Crossref] [PubMed]

Song, S.

S. Song, Y. Cao, Y. B. Sheng, and G. L. Long, “Complete Greenberger-Horne-Zeilinger state analyzer using hyperentanglement,” Quantum Inf. Process. 12, 381–393 (2013).
[Crossref]

SoutoRibeiro, P. H.

S. P. Walborn, M. P. Almeida, P. H. SoutoRibeiro, and C. H. Monken, “Quantum information processing with hyperentangled photon states,” Quantum Inform. Comput. 6, 336–350 (2006).

Steinberg, A. M.

A. Feizpour, X. Xing, and A. M. Steinberg, “Amplifying single-photon nonlinearity using weak measurements,” Phys. Rev. Lett. 107, 133603 (2011).
[Crossref] [PubMed]

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 (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 Exter, M. P.

C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat, D. P. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett. 104, 160503 (2010).
[Crossref] [PubMed]

Vedral, V.

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

Vuckovic, J.

E. Waks and J. Vuckovic, “Dipole induced transparency in drop-filter cavity-waveguide systems,” Phys. Rev. Lett. 96, 153601 (2006).
[Crossref] [PubMed]

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E. Waks and J. Vuckovic, “Dipole induced transparency in drop-filter cavity-waveguide systems,” Phys. Rev. Lett. 96, 153601 (2006).
[Crossref] [PubMed]

Walborn, S. P.

S. P. Walborn, M. P. Almeida, P. H. SoutoRibeiro, and C. H. Monken, “Quantum information processing with hyperentangled photon states,” Quantum Inform. Comput. 6, 336–350 (2006).

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[Crossref]

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T. J. Wang, C. Cao, and C. Wang, “Linear-optical implementation of hyperdistillation from photon loss,” Phys. Rev. A 89, 052303 (2014).
[Crossref]

C. Wang, Y. Zhan, and G. S. Jin, “Polarization-entanglement purification and concentration using cross-Kerr nonlinearity,” Quantum Inform. Comput. 11, 988–1002 (2011).

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[Crossref]

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T. J. Wang, C. Cao, and C. Wang, “Linear-optical implementation of hyperdistillation from photon loss,” Phys. Rev. A 89, 052303 (2014).
[Crossref]

Wei, H. R.

B. C. Ren, H. R. Wei, and F. G. Deng, “Deterministic photonic spatial-polarization hyper-controlled-not gate assisted by a quantum dot inside a one-side optical microcavity,” Laser phys. Lett. 10, 095202 (2013).
[Crossref]

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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]

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[Crossref] [PubMed]

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[Crossref]

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Wootters, W. K.

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

Xing, X.

A. Feizpour, X. Xing, and A. M. Steinberg, “Amplifying single-photon nonlinearity using weak measurements,” Phys. Rev. Lett. 107, 133603 (2011).
[Crossref] [PubMed]

Yamamoto, T.

T. Yamamoto, M. Koashi, and N. Imoto, “Concentration and purification scheme for two partially entangled photon pairs,” Phys. Rev. A 64, 012304 (2001).
[Crossref]

Yildiz, A.

A. Yildiz, “Optimal distillation of three-qubit W states,” Phys. Rev. A 82, 012317 (2010).
[Crossref]

Zeng, Z.

X. Chen, Z. Zeng, and X. H. Li, “Hyperconcentration based on projection measurements,” Commun. Theor. Phys. 61, 322–328 (2014).
[Crossref]

X. H. Li, X. Chen, and Z. Zeng, “Hyperconcentration for entanglement in two degrees of freedom,” J. Opt. Soc. Am. B 30, 2774–2780 (2013).
[Crossref]

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

Zhan, Y.

C. Wang, Y. Zhan, and G. S. Jin, “Polarization-entanglement purification and concentration using cross-Kerr nonlinearity,” Quantum Inform. Comput. 11, 988–1002 (2011).

Zhao, S. M.

Y. B. Sheng, L. Zhou, S. M. Zhao, and B. Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A 85, 012307 (2012).
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Y. B. Sheng, L. Zhou, and S. M. Zhao, “Efficient two-step entanglement concentration for arbitrary W states,” Phys. Rev. A 85, 042302 (2012).
[Crossref]

Zhao, Z.

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

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Y. B. Sheng, L. Zhou, S. M. Zhao, and B. Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A 85, 012307 (2012).
[Crossref]

Zhou, H. Y.

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Single-photon entanglement concentration for long-distance quantum communication,” Quantum Inform. Comput. 10, 0272 (2010).

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics,” Phys. Rev. A 77, 062325 (2008).
[Crossref]

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics,” Phys. Rev. A 77, 062325 (2008).
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Zhou, L.

Y. B. Sheng and L. Zhou, “Quantum entanglement concentration based on nonlinear optics for quantum communications,” Entropy 15, 1776–1820 (2013).
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Y. B. Sheng, L. Zhou, and S. M. Zhao, “Efficient two-step entanglement concentration for arbitrary W states,” Phys. Rev. A 85, 042302 (2012).
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Y. B. Sheng, L. Zhou, S. M. Zhao, and B. Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A 85, 012307 (2012).
[Crossref]

Zhu, C.

Zoller, P.

H. J. Briege, W. Dür, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932–5935 (1998).
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Commun. Theor. Phys. (1)

X. Chen, Z. Zeng, and X. H. Li, “Hyperconcentration based on projection measurements,” Commun. Theor. Phys. 61, 322–328 (2014).
[Crossref]

Entropy (1)

Y. B. Sheng and L. Zhou, “Quantum entanglement concentration based on nonlinear optics for quantum communications,” Entropy 15, 1776–1820 (2013).
[Crossref]

J. Mod. Opt (1)

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[Crossref]

J. Opt. Soc. Am. B (2)

Laser phys. Lett. (2)

X. H. Li and S. Ghose, “Hyperconcentration for multipartite entanglement via linear optics,” Laser phys. Lett. 11, 125201 (2014).
[Crossref]

B. C. Ren and F. G. Deng, “Hyperentanglement purification and concentration assisted by diamond NV centers inside photonic crystal cavities,” Laser Phys. Lett. 10, 115201 (2013).
[Crossref]

B. C. Ren, H. R. Wei, and F. G. Deng, “Deterministic photonic spatial-polarization hyper-controlled-not gate assisted by a quantum dot inside a one-side optical microcavity,” Laser phys. Lett. 10, 095202 (2013).
[Crossref]

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]

Opt. Express (2)

Phys. Rev A (1)

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[Crossref]

Phys. Rev. A (26)

B. S. Shi, Y. K. Jiang, and G. C. Guo, “Optimal entanglement purification via entanglement swapping,” Phys. Rev. A 62, 054301 (2000).
[Crossref]

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Y. B. Sheng, L. Zhou, and S. M. Zhao, “Efficient two-step entanglement concentration for arbitrary W states,” Phys. Rev. A 85, 042302 (2012).
[Crossref]

F. G. Deng, “Optimal nonlocal multipartite entanglement concentration based on projection measurements,” Phys. Rev. A 85, 022311 (2012).
[Crossref]

Y. B. Sheng, L. Zhou, S. M. Zhao, and B. Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A 85, 012307 (2012).
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[Crossref]

C. Wang, F. G. Deng, Y. S. Li, X. S. Liu, and G. L. Long, “Quantum secure direct communication with highdimension quantum superdense coding,” Phys. Rev. A 71, 044305 (2005).
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[Crossref] [PubMed]

T. Yamamoto, M. Koashi, and N. Imoto, “Concentration and purification scheme for two partially entangled photon pairs,” Phys. Rev. A 64, 012304 (2001).
[Crossref]

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

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics,” Phys. Rev. A 77, 062325 (2008).
[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 (2009)
[Crossref]

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics,” Phys. Rev. A 77, 062325 (2008).
[Crossref]

Y. B. Sheng and F. G. Deng, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A 81, 032307 (2010).
[Crossref]

X. H. Li, “Deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044304 (2010).
[Crossref]

Y. B. Sheng and F. G. Deng, “One-step deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044305 (2010).
[Crossref]

F. G. Deng, “One-step error correction for multipartite polarization entanglement,” Phys. Rev. A 83, 062316 (2011).
[Crossref]

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

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

B. C. Ren, F. F. Du, and F. G. Deng, “Hyperentanglement concentration for two-photon four-qubit systems with linear optics”, Phys. Rev. A 88, 012302 (2013).
[Crossref]

E. Shahmoon, G. Kurizki, M. Fleischhauer, and D. Petrosyan, “Strongly interacting photons in hollow-core waveguides,” Phys. Rev. A 83, 033806 (2011).
[Crossref]

T. J. Wang, C. Cao, and C. Wang, “Linear-optical implementation of hyperdistillation from photon loss,” Phys. Rev. A 89, 052303 (2014).
[Crossref]

Phys. Rev. Lett. (14)

C. Simon and J. W. Pan, “Polarization entanglement purification using spatial entanglement,” Phys. Rev. Lett. 89, 257901 (2002).
[Crossref] [PubMed]

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

A. Feizpour, X. Xing, and A. M. Steinberg, “Amplifying single-photon nonlinearity using weak measurements,” Phys. Rev. Lett. 107, 133603 (2011).
[Crossref] [PubMed]

A. V. Gorshkov, J. Otterbach, M. Fleischhauer, T. Pohl, and M. D. Lukin, “Photon-photon interactions via Rydberg blockade,” Phys. Rev. Lett. 107, 133602 (2011).
[Crossref] [PubMed]

E. Waks and J. Vuckovic, “Dipole induced transparency in drop-filter cavity-waveguide systems,” Phys. Rev. Lett. 96, 153601 (2006).
[Crossref] [PubMed]

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] [PubMed]

C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat, D. P. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett. 104, 160503 (2010).
[Crossref] [PubMed]

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

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]

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

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

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[Crossref]

A. K. Ekert, “Quantum cryptography based on Bells theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
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C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bells theorem,” Phys. Rev. Lett. 68, 557–559 (1992).
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Physics Letters A (1)

X. F. Ren, G. P. Guo, and G. C. Guo, “Complete Bell-states analysis using hyper-entanglement,” Physics Letters A 343, 8–11 (2005).
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Quantum Inf. Process. (1)

S. Song, Y. Cao, Y. B. Sheng, and G. L. Long, “Complete Greenberger-Horne-Zeilinger state analyzer using hyperentanglement,” Quantum Inf. Process. 12, 381–393 (2013).
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Quantum Inform. Comput. (3)

Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Single-photon entanglement concentration for long-distance quantum communication,” Quantum Inform. Comput. 10, 0272 (2010).

C. Wang, Y. Zhan, and G. S. Jin, “Polarization-entanglement purification and concentration using cross-Kerr nonlinearity,” Quantum Inform. Comput. 11, 988–1002 (2011).

S. P. Walborn, M. P. Almeida, P. H. SoutoRibeiro, and C. H. Monken, “Quantum information processing with hyperentangled photon states,” Quantum Inform. Comput. 6, 336–350 (2006).

Rev. Mod. Phys. (1)

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

Sci. Rep. (1)

B. C. Ren and F. G. Deng, “Hyper-parallel photonic quantum computation with coupled quantum dots,” Sci. Rep. 4, 4623 (2014).
[Crossref] [PubMed]

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Figures (6)

Fig. 1
Fig. 1 The schematic diagram of the polarization parity check device based on the cross-Kerr nonlinearity. Polarizing beam splitters (PBSs) are used to transmit the horizontal polarization |H〉 and reflect the vertical polarization |V〉. ±θ = χt represent the cross-Kerr nonlinear media that introduce the phase shift θ when there is a photon passing through the media. 〉 〈χ| is the homodyne measurement that can distinguish different phase shifts.
Fig. 2
Fig. 2 The schematic diagram of the spatial mode parity check device that is used to check the parity of the spatial modes of photons i and j. ±θ represent the cross-Kerr nonlinear media which introduce the phase shift θ when there is a photon passing through the media. 〉 〈χ| is the homodyne measurement that can discriminate different phase shifts.
Fig. 3
Fig. 3 Schematic diagram of the proposed hyperconcentration protocol assisted by an auxiliary photon. An additional photon X is prepared by Alice based on the parameters of the original state. Then the PPC and SPC are performed on Alice’s two photons A and X and the particle X is measured in the diagonal basis of both DOFs, denoted by M. By selecting only even-parity outcomes in both the DOFs and then measuring the additional photon in the diagonal basis, the remote N parities share the maximally hyperentangled GHZ state with a certain probability.
Fig. 4
Fig. 4 Schematic diagram of the single-photon two-qubit measurement. Both the two DOFs of the single photon are measured in the diagonal basis. The measurement of spatial mode is realized by the beam splitter (BS) and of the polarization state is implemented by PBS at 45°. The effect of the balanced BS is | u 1 2 ( | u + | d ), | d 1 2 ( | u | d ).
Fig. 5
Fig. 5 Schematic diagram of the proposed hyperconcentration protocol which distills maximal hyperentanglement from two identical less-entangled nonlocal N-photon GHZ states (solid and dotted). Alice performs a PPC and SPC on her photons A1 and A2 to check the parity of the polarization and spatial mode DOFs and then measures A2. The other N−1 parties (Bob, Charlie, etc) perform single-photon two-qubit measurements on their second photons. By selecting on the even-parity results of Alice’s two parity checks, the distant N parties share the maximally hyperentangled state probabilistically.
Fig. 6
Fig. 6 The total success probability of obtaining the maximally hyperentangled state depends on the parameters of the initial state |α|2 and |δ|2. Different Figs. correspond to the schemes with different number of iterations.

Tables (1)

Tables Icon

Table 1 The normalized coefficients for the three less-entangled states corresponding to the failed instances of the parity checks.

Equations (30)

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

H = h ¯ χ a s a s a p a p .
| α p | α e i n θ ,
| Ψ A B C = ( α | H H H + β | V V V ) ( δ | a u b u c u + η | a d b d c d ) .
| Φ A B C = 1 2 ( | H H H + | V V V ) 1 2 ( | a u b u c u + | a d b d c d ) .
| φ X = ( α | V + β | H ) X ( δ | x d + η | x u ) X .
| Ψ A B C X = [ α 2 | H H H V + β 2 | V V V H + α β ( | H H H H + | V V V V ) ] [ δ 2 | a u b u c u x d + η 2 | a d b d c d x u + δ η ( | a u b u c u x u + | a d b d c d x d ) ] .
| Ψ A B C X = α β δ η ( | H H H H + | V V V V ) ] ( | a u b u c u x u + | a d b d c d x d ) .
| Ψ A B C = α β δ η ( | H H H ± | V V V ) ] ( | a u b u c u ± | a d b d c d ) .
| Ψ A 2 B 2 C 2 = ( α | V V V + β | H H H ) ( δ | a 2 d b 2 d c 2 d + η | a 2 u b 2 u c 2 u ) .
| Ξ A 1 B 1 C 1 A 2 B 2 C 2 = [ α 2 | H H H V V V + β 2 | V V V H H H + α β ( | H H H H H H + | V V V V V V ) ] [ δ 2 | a 1 u b 1 u c 1 u a 2 d b 2 d c 2 d + η 2 | a 1 d b 1 d c 1 d a 2 u b 2 u c 2 u + δ η ( | a 1 u b 1 u c 1 u a 2 u b 2 u c 2 u + | a 1 d b 1 d c 1 d a 2 d b 2 d c 2 d ) ] .
| Ξ A 1 B 1 C 1 A 2 B 2 C 2 = α β δ η ( | H H H H H H + | V V V V V V ) ( | a 1 u b 1 u c 1 u a 2 u b 2 u c 2 u + | a 1 d b 1 d c 1 d a 2 d b 2 d c 2 d ) .
| Ξ A 1 B 1 C 1 = 1 2 ( | H H H + ( 1 ) P | V V V ) ( | a 1 u b 1 u c 1 u + ( 1 ) Q | a 1 d b 1 d c 1 d ) .
| Ψ e o A B C = α β ( | H H H + | V V V ) ( δ 2 | a u b u c u + η 2 | a d b d c d ) ,
| Ψ o e A B C = ( α 2 | H H H + β 2 | V V V ) δ η ( | a u b u c u + | a d b d c d ) ,
| Ψ o o A B C = ( α 2 | H H H + β 2 | V V V ) ( δ 2 | a u b u c u + η 2 | a d b d c d ) .
P e o ( 1 ) = 2 | α | 2 | β | 2 ( | δ | 4 + | η | 4 ) ,
P o e ( 1 ) = 2 | δ | 2 | η | 2 ( | α | 4 + | β | 4 ) ,
P o o ( 1 ) = ( | α | 4 + | β | 4 ) ( | δ | 4 + | η | 4 ) .
| Ψ ( 2 ) A B C = ( α i ( 2 ) | H H H + β i ( 2 ) | V V V ) ( δ i ( 2 ) | a u b u c u + η i ( 2 ) | a d b d c d ) .
P ( 2 ) = P e o ( 1 ) ( P e o e e ( 2 ) + P e o o e ( 2 ) ) + P o e ( 1 ) ( P o e e e ( 2 ) + P o e e o ( 2 ) ) + P o o ( 1 ) P o o e e ( 2 )
P e o , s ( k ) = P e o e e ( k ) + P e o o e ( k ) = 2 | δ η | 2 k ( | δ | 2 k + | η | 2 k ) 2 ,
P e o , f ( k ) = P e o e o ( k ) + P e o o o ( k ) = | δ | 2 k + 1 + | η | 2 k + 1 ( | δ | 2 k + | η | 2 k ) 2 ,
P o e , s ( k ) = P o e e e ( k ) + P o e e o ( k ) = 2 | α β | 2 k ( | α | 2 k + | β | 2 k ) 2 ,
P o e , f ( k ) = P o e o e ( k ) + P o e o o ( k ) = | α | 2 k + 1 + | β | 2 k + 1 ( | α | 2 k + | β | 2 k ) 2 .
P o o e e ( k ) = 4 | α β δ η | 2 k ( | α | 2 k + | β | 2 k ) 2 ( | δ | 2 k + | η | 2 k ) 2 = P e o , s ( k ) P o e , s ( k ) ,
P o o o e ( k ) = 2 | α β | 2 k ( | δ | 2 k + 1 + | η | 2 k + 1 ) ( | α | 2 k + | β | 2 k ) 2 ( | δ | 2 k + | η | 2 k ) 2 = P e o , f ( k ) P o e , s ( k ) ,
P o o o e ( k ) = 2 | δ η | 2 k ( | α | 2 k + 1 + | β | 2 k + 1 ) ( | α | 2 k + | β | 2 k ) 2 ( | δ | 2 k + | η | 2 k ) 2 = P e o , s ( k ) P o e , f ( k ) ,
P o o o o ( k ) = ( | α | 2 k + 1 + | β | 2 k + 1 ) ( | δ | 2 k + 1 + | η | 2 k + 1 ) ( | α | 2 k + | β | 2 k ) 2 ( | δ | 2 k + | η | 2 k ) 2 = P e o , f ( k ) P o e , f ( k ) .
P ( k ) = [ P e o ( 1 ) + P o o ( 1 ) ( P o e , s ( 2 ) + P o e , f ( 2 ) P o e , s ( 3 ) + P o e , f ( 2 ) P o e , f ( 3 ) P o e , f ( k 2 ) P o e , s ( k 1 ) ) ] P e o , f ( 2 ) P e o , f ( k 1 ) P e o , s ( k ) + P o e ( 1 ) + P o o ( 1 ) ( P e o , s ( 2 ) + P e o , f ( 2 ) P e o , s ( 3 ) + P e o , f ( 2 ) P e o , f ( 3 ) P e o , f ( k 2 ) P e o , s ( k 1 ) ) ] P o e , f ( 2 ) P e o , f ( k 1 ) P o e , s ( k ) + P o o ( 1 ) P e o , f ( 2 ) P o e , f ( 2 ) P e o , f ( 3 ) P o e , f ( 3 ) P e o , f ( k 1 ) P o e , f ( k 1 ) P e o , s ( k ) P o e , s ( k ) .
P T o t a l = k = 1 n P ( k ) ,

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