Abstract

We investigate a new approach for achieving hyperdistillation and hyperentanglement purification operations simultaneously on two-photon systems, whose state is described by nonlocal hyperentangled Bell states on both the spatial mode and polarization degree of freedoms. Exploiting linear optics and local entanglement resource, the quantum nondemolition (QND) parity-checking measurement and the heralded two-qubit amplification could are key steps in our scheme. With the QND parity-checking measurement and heralded qubit amplification operations, both the bit-flip (phase-flip) errors caused by decoherence in noisy channels and the vacuum errors caused by the transmission losses can be corrected. We show that the proposed scheme provides a new solution to overcome the problem of photon losses and decoherence simultaneously, which could be achieved with current technologies.

© 2015 Optical Society of America

Full Article  |  PDF Article
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    [Crossref]
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    [Crossref] [PubMed]
  5. X. S. Liu, G. L. Long, D. M. Tong, and Feng Li, “General scheme for superdense coding between multiparties,” Phys. Rev. A 65, 022304 (2002).
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  6. A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661 (1991).
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  7. C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bells theorem,” Phys. Rev. Lett. 68, 557 (1992).
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  8. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145 (2002).
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  12. R. Heilmann, M. Gräfe, S Nolte, and A Szameit, “A novel integrated quantum circuit for high-order W-state generation and its highly precise characterization,” Sci. Bull. 60, 96(2015).
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  14. N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
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  15. M. M. Wilde and D. B. Uskov, “Linear-optical hyperentanglement assisted quantum error-correcting code,” Phys. Rev. A 79, 022305 (2009).
    [Crossref]
  16. 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]
  17. B. C. Ren and G. L. Long, “General hyperentanglement concentration for photon systems assisted by quantum-dot spins inside optical microcavities, ” Optics express 22, 6547 (2014).
    [Crossref] [PubMed]
  18. Y. B. Sheng, J. Liu, S. Y. Zhao, and L. Zhou, “Multipartite entanglement concentration for nitrogen-vacancy center and microtoroidal resonator system, ” Chin. Sci. Bull. 59, 3507 (2013).
    [Crossref]
  19. C. Wang, L. Y. He, Y. Zhang, H. Q. Ma, and R. Zhang, “Complete entanglement analysis on electron spins using quantum dot and microcavity coupled system, ” Sci. China- Phys Mech Astron 56, 2054 (2013).
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  20. T. J. Wang, Y. Lu, and G. L. Long, “Generation and complete analysis of the hyperentangled Bell state for photons assisted by quantum-dot spins in optical microcavities, ” Phys. Rev. A 86, 042337 (2012).
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    [Crossref]
  24. P. M. Pearle, “Hidden-variable example based upon data rejection,” Phys. Rev. D 2, 1418 (1970).
    [Crossref]
  25. J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880 (1969).
    [Crossref]
  26. A. Cabello and F. Sciarrino, “Loophole-free Bell test based on local precertification of photons presence,” Phys. Rev. X. 2, 021010 (2012).
  27. C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722 (1996).
    [Crossref] [PubMed]
  28. D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 77, 2818(1996).
    [Crossref] [PubMed]
  29. J. W. Pan, C. Simon, C. Brukner, and A. Zelinger, “Entanglement purification,” Nature(London). 410, 1067 (2001).
    [Crossref]
  30. C. Simon and J. W. Pan, “Polarization entanglement purification using spatial entanglement,” Phys. Rev. A 89, 257901 (2002).
  31. W. Dür, H. Aschauer, and H. J. Briegel, “Multiparticle entanglement purification for graph states,” Phys. Rev. Lett. 91, 107903 (2003).
    [Crossref] [PubMed]
  32. M. Horodecki and P. Horodecki, “Reduction criterion of separability and limits for a class of distillation protocols,” Phys. Rev. A 59, 4206 (1999).
    [Crossref]
  33. A. Miyake and H. J. Briegel, “Distillation of multipartite entanglement by complementary stabilizer measurements,” Phys. Rev. Lett. 95, 220501 (2005).
    [Crossref] [PubMed]
  34. Y. W. Cheong, S. W. Lee, J. Lee, and H. -W. Lee, “Entanglement purification for high-dimensional multipartite systems,” Phys. Rev. A. 76, 042314 (2007).
    [Crossref]
  35. S. Y. Hou, Y. B. Sheng, G. R. Feng, and G. L. Long, “Experimental Optimal Single Qubit Purification in an NMR Quantum Information Processor,” Scientific reports 4, 6857(2014).
    [Crossref] [PubMed]
  36. Y. Liu and J. X. Cui, “Realization of Kraus operators and POVM measurements using a duality quantum computer,” Chin. Sci. Bull. 59, 2298(2014).
    [Crossref]
  37. C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046 (1996).
    [Crossref] [PubMed]
  38. H. K. Lo and S. Popescu, “Concentrating entanglement by local actions: Beyond mean values,” Phys. Rev. A 63, 022301 (2001).
    [Crossref]
  39. T. J. Wang and G. L. Long, “Entanglement concentration for arbitrary unknown less-entangled three-photon W states with linear optics,” J. Opt. Soc. Am. B 30, 1069 (2013).
    [Crossref]
  40. 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]
  41. After the linear optical entanglement purification operation [23] in polarization DOF on the photon-pairs AB and A1B1, the final state of the resived photon-pair A′B′ is ρA′B′=1T1T2[f2+(1−f)2]+(1−T1)T2+(1−T2)T1+(1−T1)(1−T2)(2f+1){(1−T1)(1−T2)(2f+1)2|vac,vac〉A′B′〈vac|+(1−T1)T24|vac〉A′〈vac|⊗[f|H〉B′〈H|+(1−f)|V〉B′〈V|]+T1(1−T2)4|vac〉A′〈vac|⊗[f|V〉B′〈V|+(1−f)|H〉B′〈H|]+(1−T1)T24|vac〉B′〈vac|⊗[f|V〉A′〈V|+(1−f)|H〉A′〈H|]+T1(1−T2)4|vac〉B′〈vac|⊗[f|H〉A′〈H|+(1−f)|V〉A′〈V|]+T1T2[f2+(1−f)2]2[f′|ϕ+〉A′B′〈ϕ++(1−f′)|ψ+〉A′B′〈ψ+||]}, where f′=f2f2+(1−f)2.
  42. N. Gisin, S. Pironio, and N. Sangouard, “Proposal for implementing device-independent quantum key distribution based on a heralded qubit amplifier,” Phys. Rev. Lett. 105, 070501 (2010).
    [Crossref] [PubMed]

2015 (1)

R. Heilmann, M. Gräfe, S Nolte, and A Szameit, “A novel integrated quantum circuit for high-order W-state generation and its highly precise characterization,” Sci. Bull. 60, 96(2015).
[Crossref]

2014 (4)

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

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

S. Y. Hou, Y. B. Sheng, G. R. Feng, and G. L. Long, “Experimental Optimal Single Qubit Purification in an NMR Quantum Information Processor,” Scientific reports 4, 6857(2014).
[Crossref] [PubMed]

Y. Liu and J. X. Cui, “Realization of Kraus operators and POVM measurements using a duality quantum computer,” Chin. Sci. Bull. 59, 2298(2014).
[Crossref]

2013 (4)

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]

Y. B. Sheng, J. Liu, S. Y. Zhao, and L. Zhou, “Multipartite entanglement concentration for nitrogen-vacancy center and microtoroidal resonator system, ” Chin. Sci. Bull. 59, 3507 (2013).
[Crossref]

C. Wang, L. Y. He, Y. Zhang, H. Q. Ma, and R. Zhang, “Complete entanglement analysis on electron spins using quantum dot and microcavity coupled system, ” Sci. China- Phys Mech Astron 56, 2054 (2013).
[Crossref]

T. J. Wang and G. L. Long, “Entanglement concentration for arbitrary unknown less-entangled three-photon W states with linear optics,” J. Opt. Soc. Am. B 30, 1069 (2013).
[Crossref]

2012 (2)

T. J. Wang, Y. Lu, and G. L. Long, “Generation and complete analysis of the hyperentangled Bell state for photons assisted by quantum-dot spins in optical microcavities, ” Phys. Rev. A 86, 042337 (2012).
[Crossref]

A. Cabello and F. Sciarrino, “Loophole-free Bell test based on local precertification of photons presence,” Phys. Rev. X. 2, 021010 (2012).

2010 (3)

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]

N. Gisin, S. Pironio, and N. Sangouard, “Proposal for implementing device-independent quantum key distribution based on a heralded qubit amplifier,” Phys. Rev. Lett. 105, 070501 (2010).
[Crossref] [PubMed]

H. Buhrman, R. Cleve, S. Massar, and R. de Wolf, “Nonlocality and communication complexity,” Rev. Mod. Phys. 82, 665 (2010).
[Crossref]

2009 (2)

W. Y. Wang, C. Wang, G. Y. Zhang, and G. L. Long, “Arbitrarily long distance quantum communication using inspection and power insertion,” Chin. Sci. Bull. 54, 158 (2009).
[Crossref]

M. M. Wilde and D. B. Uskov, “Linear-optical hyperentanglement assisted quantum error-correcting code,” Phys. Rev. A 79, 022305 (2009).
[Crossref]

2007 (1)

Y. W. Cheong, S. W. Lee, J. Lee, and H. -W. Lee, “Entanglement purification for high-dimensional multipartite systems,” Phys. Rev. A. 76, 042314 (2007).
[Crossref]

2006 (1)

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).
[Crossref]

2005 (1)

A. Miyake and H. J. Briegel, “Distillation of multipartite entanglement by complementary stabilizer measurements,” Phys. Rev. Lett. 95, 220501 (2005).
[Crossref] [PubMed]

2004 (1)

L. Xiao, G. L. Long, F.-G. Deng, and J. -W. Pan, “Efficient multiparty quantum-secret-sharing schemes,” Phys. Rev. A 69, 052307 (2004).
[Crossref]

2003 (1)

W. Dür, H. Aschauer, and H. J. Briegel, “Multiparticle entanglement purification for graph states,” Phys. Rev. Lett. 91, 107903 (2003).
[Crossref] [PubMed]

2002 (6)

C. Simon and J. W. Pan, “Polarization entanglement purification using spatial entanglement,” Phys. Rev. A 89, 257901 (2002).

X. S. Liu, G. L. Long, D. M. Tong, and Feng Li, “General scheme for superdense coding between multiparties,” Phys. Rev. A 65, 022304 (2002).
[Crossref]

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

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

D. Bruss and C. Macchiavello, “Optimal eavesdropping in cryptography with three-dimensional quantum states,” Phys. Rev. Lett. 88, 127901 (2002).
[Crossref] [PubMed]

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[Crossref] [PubMed]

2001 (2)

J. W. Pan, C. Simon, C. Brukner, and A. Zelinger, “Entanglement purification,” Nature(London). 410, 1067 (2001).
[Crossref]

H. K. Lo and S. Popescu, “Concentrating entanglement by local actions: Beyond mean values,” Phys. Rev. A 63, 022301 (2001).
[Crossref]

1999 (2)

M. Horodecki and P. Horodecki, “Reduction criterion of separability and limits for a class of distillation protocols,” Phys. Rev. A 59, 4206 (1999).
[Crossref]

M. Hillery and V. Bužek, “Quantum secret sharing,” Phys. Rev. A 59, 1829 (1999).
[Crossref]

1996 (3)

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

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722 (1996).
[Crossref] [PubMed]

D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 77, 2818(1996).
[Crossref] [PubMed]

1992 (2)

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

1991 (1)

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

1970 (1)

P. M. Pearle, “Hidden-variable example based upon data rejection,” Phys. Rev. D 2, 1418 (1970).
[Crossref]

1969 (1)

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880 (1969).
[Crossref]

Aschauer, H.

W. Dür, H. Aschauer, and H. J. Briegel, “Multiparticle entanglement purification for graph states,” Phys. Rev. Lett. 91, 107903 (2003).
[Crossref] [PubMed]

Bell, J. S.

J. S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge University, 1987).

Bennett, C. H.

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722 (1996).
[Crossref] [PubMed]

C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046 (1996).
[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 (1992).
[Crossref] [PubMed]

C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bells theorem,” Phys. Rev. Lett. 68, 557 (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 (1996).
[Crossref] [PubMed]

Bourennane, M.

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[Crossref] [PubMed]

Brassard, G.

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722 (1996).
[Crossref] [PubMed]

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

Briegel, H. J.

A. Miyake and H. J. Briegel, “Distillation of multipartite entanglement by complementary stabilizer measurements,” Phys. Rev. Lett. 95, 220501 (2005).
[Crossref] [PubMed]

W. Dür, H. Aschauer, and H. J. Briegel, “Multiparticle entanglement purification for graph states,” Phys. Rev. Lett. 91, 107903 (2003).
[Crossref] [PubMed]

Brukner, C.

J. W. Pan, C. Simon, C. Brukner, and A. Zelinger, “Entanglement purification,” Nature(London). 410, 1067 (2001).
[Crossref]

Bruss, D.

D. Bruss and C. Macchiavello, “Optimal eavesdropping in cryptography with three-dimensional quantum states,” Phys. Rev. Lett. 88, 127901 (2002).
[Crossref] [PubMed]

Buhrman, H.

H. Buhrman, R. Cleve, S. Massar, and R. de Wolf, “Nonlocality and communication complexity,” Rev. Mod. Phys. 82, 665 (2010).
[Crossref]

Bužek, V.

M. Hillery and V. Bužek, “Quantum secret sharing,” Phys. Rev. A 59, 1829 (1999).
[Crossref]

Cabello, A.

A. Cabello and F. Sciarrino, “Loophole-free Bell test based on local precertification of photons presence,” Phys. Rev. X. 2, 021010 (2012).

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]

Cerf, N. J.

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[Crossref] [PubMed]

Cheong, Y. W.

Y. W. Cheong, S. W. Lee, J. Lee, and H. -W. Lee, “Entanglement purification for high-dimensional multipartite systems,” Phys. Rev. A. 76, 042314 (2007).
[Crossref]

Chuang, I. L.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).

Clauser, J. F.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880 (1969).
[Crossref]

Cleve, R.

H. Buhrman, R. Cleve, S. Massar, and R. de Wolf, “Nonlocality and communication complexity,” Rev. Mod. Phys. 82, 665 (2010).
[Crossref]

Cui, J. X.

Y. Liu and J. X. Cui, “Realization of Kraus operators and POVM measurements using a duality quantum computer,” Chin. Sci. Bull. 59, 2298(2014).
[Crossref]

de Wolf, R.

H. Buhrman, R. Cleve, S. Massar, and R. de Wolf, “Nonlocality and communication complexity,” Rev. Mod. Phys. 82, 665 (2010).
[Crossref]

Deng, F. G.

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]

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]

Deng, F. -G.

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).
[Crossref]

Deng, F.-G.

L. Xiao, G. L. Long, F.-G. Deng, and J. -W. Pan, “Efficient multiparty quantum-secret-sharing schemes,” Phys. Rev. A 69, 052307 (2004).
[Crossref]

Deutsch, D.

D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 77, 2818(1996).
[Crossref] [PubMed]

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.

W. Dür, H. Aschauer, and H. J. Briegel, “Multiparticle entanglement purification for graph states,” Phys. Rev. Lett. 91, 107903 (2003).
[Crossref] [PubMed]

Ekert, A.

D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 77, 2818(1996).
[Crossref] [PubMed]

Ekert, A. K.

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

Feng, G. R.

S. Y. Hou, Y. B. Sheng, G. R. Feng, and G. L. Long, “Experimental Optimal Single Qubit Purification in an NMR Quantum Information Processor,” Scientific reports 4, 6857(2014).
[Crossref] [PubMed]

Gisin, N.

N. Gisin, S. Pironio, and N. Sangouard, “Proposal for implementing device-independent quantum key distribution based on a heralded qubit amplifier,” Phys. Rev. Lett. 105, 070501 (2010).
[Crossref] [PubMed]

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

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[Crossref] [PubMed]

Gräfe, M.

R. Heilmann, M. Gräfe, S Nolte, and A Szameit, “A novel integrated quantum circuit for high-order W-state generation and its highly precise characterization,” Sci. Bull. 60, 96(2015).
[Crossref]

He, L. Y.

C. Wang, L. Y. He, Y. Zhang, H. Q. Ma, and R. Zhang, “Complete entanglement analysis on electron spins using quantum dot and microcavity coupled system, ” Sci. China- Phys Mech Astron 56, 2054 (2013).
[Crossref]

Heilmann, R.

R. Heilmann, M. Gräfe, S Nolte, and A Szameit, “A novel integrated quantum circuit for high-order W-state generation and its highly precise characterization,” Sci. Bull. 60, 96(2015).
[Crossref]

Hillery, M.

M. Hillery and V. Bužek, “Quantum secret sharing,” Phys. Rev. A 59, 1829 (1999).
[Crossref]

Holt, R. A.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880 (1969).
[Crossref]

Horne, M. A.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880 (1969).
[Crossref]

Horodecki, M.

M. Horodecki and P. Horodecki, “Reduction criterion of separability and limits for a class of distillation protocols,” Phys. Rev. A 59, 4206 (1999).
[Crossref]

Horodecki, P.

M. Horodecki and P. Horodecki, “Reduction criterion of separability and limits for a class of distillation protocols,” Phys. Rev. A 59, 4206 (1999).
[Crossref]

Hou, S. Y.

S. Y. Hou, Y. B. Sheng, G. R. Feng, and G. L. Long, “Experimental Optimal Single Qubit Purification in an NMR Quantum Information Processor,” Scientific reports 4, 6857(2014).
[Crossref] [PubMed]

Jozsa, R.

D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 77, 2818(1996).
[Crossref] [PubMed]

Karlsson, A.

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[Crossref] [PubMed]

Lee, H. -W.

Y. W. Cheong, S. W. Lee, J. Lee, and H. -W. Lee, “Entanglement purification for high-dimensional multipartite systems,” Phys. Rev. A. 76, 042314 (2007).
[Crossref]

Lee, J.

Y. W. Cheong, S. W. Lee, J. Lee, and H. -W. Lee, “Entanglement purification for high-dimensional multipartite systems,” Phys. Rev. A. 76, 042314 (2007).
[Crossref]

Lee, S. W.

Y. W. Cheong, S. W. Lee, J. Lee, and H. -W. Lee, “Entanglement purification for high-dimensional multipartite systems,” Phys. Rev. A. 76, 042314 (2007).
[Crossref]

Li, Feng

X. S. Liu, G. L. Long, D. M. Tong, and Feng Li, “General scheme for superdense coding between multiparties,” Phys. Rev. A 65, 022304 (2002).
[Crossref]

Li, X. -H.

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).
[Crossref]

Liu, J.

Y. B. Sheng, J. Liu, S. Y. Zhao, and L. Zhou, “Multipartite entanglement concentration for nitrogen-vacancy center and microtoroidal resonator system, ” Chin. Sci. Bull. 59, 3507 (2013).
[Crossref]

Liu, X. S.

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

X. S. Liu, G. L. Long, D. M. Tong, and Feng Li, “General scheme for superdense coding between multiparties,” Phys. Rev. A 65, 022304 (2002).
[Crossref]

Liu, Y.

Y. Liu and J. X. Cui, “Realization of Kraus operators and POVM measurements using a duality quantum computer,” Chin. Sci. Bull. 59, 2298(2014).
[Crossref]

Lo, H. K.

H. K. Lo and S. Popescu, “Concentrating entanglement by local actions: Beyond mean values,” Phys. Rev. A 63, 022301 (2001).
[Crossref]

Long, G. L.

S. Y. Hou, Y. B. Sheng, G. R. Feng, and G. L. Long, “Experimental Optimal Single Qubit Purification in an NMR Quantum Information Processor,” Scientific reports 4, 6857(2014).
[Crossref] [PubMed]

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

T. J. Wang and G. L. Long, “Entanglement concentration for arbitrary unknown less-entangled three-photon W states with linear optics,” J. Opt. Soc. Am. B 30, 1069 (2013).
[Crossref]

T. J. Wang, Y. Lu, and G. L. Long, “Generation and complete analysis of the hyperentangled Bell state for photons assisted by quantum-dot spins in optical microcavities, ” Phys. Rev. A 86, 042337 (2012).
[Crossref]

W. Y. Wang, C. Wang, G. Y. Zhang, and G. L. Long, “Arbitrarily long distance quantum communication using inspection and power insertion,” Chin. Sci. Bull. 54, 158 (2009).
[Crossref]

L. Xiao, G. L. Long, F.-G. Deng, and J. -W. Pan, “Efficient multiparty quantum-secret-sharing schemes,” Phys. Rev. A 69, 052307 (2004).
[Crossref]

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

X. S. Liu, G. L. Long, D. M. Tong, and Feng Li, “General scheme for superdense coding between multiparties,” Phys. Rev. A 65, 022304 (2002).
[Crossref]

Lu, Y.

T. J. Wang, Y. Lu, and G. L. Long, “Generation and complete analysis of the hyperentangled Bell state for photons assisted by quantum-dot spins in optical microcavities, ” Phys. Rev. A 86, 042337 (2012).
[Crossref]

Ma, H. Q.

C. Wang, L. Y. He, Y. Zhang, H. Q. Ma, and R. Zhang, “Complete entanglement analysis on electron spins using quantum dot and microcavity coupled system, ” Sci. China- Phys Mech Astron 56, 2054 (2013).
[Crossref]

Macchiavello, C.

D. Bruss and C. Macchiavello, “Optimal eavesdropping in cryptography with three-dimensional quantum states,” Phys. Rev. Lett. 88, 127901 (2002).
[Crossref] [PubMed]

D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 77, 2818(1996).
[Crossref] [PubMed]

Massar, S.

H. Buhrman, R. Cleve, S. Massar, and R. de Wolf, “Nonlocality and communication complexity,” Rev. Mod. Phys. 82, 665 (2010).
[Crossref]

Mermin, N. D.

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

Miyake, A.

A. Miyake and H. J. Briegel, “Distillation of multipartite entanglement by complementary stabilizer measurements,” Phys. Rev. Lett. 95, 220501 (2005).
[Crossref] [PubMed]

Nielsen, M. A.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).

Nolte, S

R. Heilmann, M. Gräfe, S Nolte, and A Szameit, “A novel integrated quantum circuit for high-order W-state generation and its highly precise characterization,” Sci. Bull. 60, 96(2015).
[Crossref]

Pan, J. W.

C. Simon and J. W. Pan, “Polarization entanglement purification using spatial entanglement,” Phys. Rev. A 89, 257901 (2002).

J. W. Pan, C. Simon, C. Brukner, and A. Zelinger, “Entanglement purification,” Nature(London). 410, 1067 (2001).
[Crossref]

Pan, J. -W.

L. Xiao, G. L. Long, F.-G. Deng, and J. -W. Pan, “Efficient multiparty quantum-secret-sharing schemes,” Phys. Rev. A 69, 052307 (2004).
[Crossref]

Pearle, P. M.

P. M. Pearle, “Hidden-variable example based upon data rejection,” Phys. Rev. D 2, 1418 (1970).
[Crossref]

Pironio, S.

N. Gisin, S. Pironio, and N. Sangouard, “Proposal for implementing device-independent quantum key distribution based on a heralded qubit amplifier,” Phys. Rev. Lett. 105, 070501 (2010).
[Crossref] [PubMed]

Popescu, S.

H. K. Lo and S. Popescu, “Concentrating entanglement by local actions: Beyond mean values,” Phys. Rev. A 63, 022301 (2001).
[Crossref]

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722 (1996).
[Crossref] [PubMed]

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

D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 77, 2818(1996).
[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, ” Optics express 22, 6547 (2014).
[Crossref] [PubMed]

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]

Ribordy, G.

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

Sangouard, N.

N. Gisin, S. Pironio, and N. Sangouard, “Proposal for implementing device-independent quantum key distribution based on a heralded qubit amplifier,” Phys. Rev. Lett. 105, 070501 (2010).
[Crossref] [PubMed]

Sanpera, A.

D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 77, 2818(1996).
[Crossref] [PubMed]

Schumacher, B.

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722 (1996).
[Crossref] [PubMed]

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

Sciarrino, F.

A. Cabello and F. Sciarrino, “Loophole-free Bell test based on local precertification of photons presence,” Phys. Rev. X. 2, 021010 (2012).

Sheng, Y. B.

S. Y. Hou, Y. B. Sheng, G. R. Feng, and G. L. Long, “Experimental Optimal Single Qubit Purification in an NMR Quantum Information Processor,” Scientific reports 4, 6857(2014).
[Crossref] [PubMed]

Y. B. Sheng, J. Liu, S. Y. Zhao, and L. Zhou, “Multipartite entanglement concentration for nitrogen-vacancy center and microtoroidal resonator system, ” Chin. Sci. Bull. 59, 3507 (2013).
[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]

Shimony, A.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880 (1969).
[Crossref]

Simon, C.

C. Simon and J. W. Pan, “Polarization entanglement purification using spatial entanglement,” Phys. Rev. A 89, 257901 (2002).

J. W. Pan, C. Simon, C. Brukner, and A. Zelinger, “Entanglement purification,” Nature(London). 410, 1067 (2001).
[Crossref]

Smolin, J. A.

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722 (1996).
[Crossref] [PubMed]

Szameit, A

R. Heilmann, M. Gräfe, S Nolte, and A Szameit, “A novel integrated quantum circuit for high-order W-state generation and its highly precise characterization,” Sci. Bull. 60, 96(2015).
[Crossref]

Tittel, W.

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

Tong, D. M.

X. S. Liu, G. L. Long, D. M. Tong, and Feng Li, “General scheme for superdense coding between multiparties,” Phys. Rev. A 65, 022304 (2002).
[Crossref]

Uskov, D. B.

M. M. Wilde and D. B. Uskov, “Linear-optical hyperentanglement assisted quantum error-correcting code,” Phys. Rev. A 79, 022305 (2009).
[Crossref]

Wang, C.

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, L. Y. He, Y. Zhang, H. Q. Ma, and R. Zhang, “Complete entanglement analysis on electron spins using quantum dot and microcavity coupled system, ” Sci. China- Phys Mech Astron 56, 2054 (2013).
[Crossref]

W. Y. Wang, C. Wang, G. Y. Zhang, and G. L. Long, “Arbitrarily long distance quantum communication using inspection and power insertion,” Chin. Sci. Bull. 54, 158 (2009).
[Crossref]

Wang, T. J.

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

T. J. Wang and G. L. Long, “Entanglement concentration for arbitrary unknown less-entangled three-photon W states with linear optics,” J. Opt. Soc. Am. B 30, 1069 (2013).
[Crossref]

T. J. Wang, Y. Lu, and G. L. Long, “Generation and complete analysis of the hyperentangled Bell state for photons assisted by quantum-dot spins in optical microcavities, ” Phys. Rev. A 86, 042337 (2012).
[Crossref]

Wang, W. Y.

W. Y. Wang, C. Wang, G. Y. Zhang, and G. L. Long, “Arbitrarily long distance quantum communication using inspection and power insertion,” Chin. Sci. Bull. 54, 158 (2009).
[Crossref]

Wiesner, S. J.

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

Wilde, M. M.

M. M. Wilde and D. B. Uskov, “Linear-optical hyperentanglement assisted quantum error-correcting code,” Phys. Rev. A 79, 022305 (2009).
[Crossref]

Wootters, W. K.

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722 (1996).
[Crossref] [PubMed]

Xiao, L.

L. Xiao, G. L. Long, F.-G. Deng, and J. -W. Pan, “Efficient multiparty quantum-secret-sharing schemes,” Phys. Rev. A 69, 052307 (2004).
[Crossref]

Zbinden, H.

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

Zelinger, A.

J. W. Pan, C. Simon, C. Brukner, and A. Zelinger, “Entanglement purification,” Nature(London). 410, 1067 (2001).
[Crossref]

Zhang, G. Y.

W. Y. Wang, C. Wang, G. Y. Zhang, and G. L. Long, “Arbitrarily long distance quantum communication using inspection and power insertion,” Chin. Sci. Bull. 54, 158 (2009).
[Crossref]

Zhang, R.

C. Wang, L. Y. He, Y. Zhang, H. Q. Ma, and R. Zhang, “Complete entanglement analysis on electron spins using quantum dot and microcavity coupled system, ” Sci. China- Phys Mech Astron 56, 2054 (2013).
[Crossref]

Zhang, Y.

C. Wang, L. Y. He, Y. Zhang, H. Q. Ma, and R. Zhang, “Complete entanglement analysis on electron spins using quantum dot and microcavity coupled system, ” Sci. China- Phys Mech Astron 56, 2054 (2013).
[Crossref]

Zhao, S. Y.

Y. B. Sheng, J. Liu, S. Y. Zhao, and L. Zhou, “Multipartite entanglement concentration for nitrogen-vacancy center and microtoroidal resonator system, ” Chin. Sci. Bull. 59, 3507 (2013).
[Crossref]

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).
[Crossref]

Zhou, L.

Y. B. Sheng, J. Liu, S. Y. Zhao, and L. Zhou, “Multipartite entanglement concentration for nitrogen-vacancy center and microtoroidal resonator system, ” Chin. Sci. Bull. 59, 3507 (2013).
[Crossref]

Chin. Sci. Bull. (3)

W. Y. Wang, C. Wang, G. Y. Zhang, and G. L. Long, “Arbitrarily long distance quantum communication using inspection and power insertion,” Chin. Sci. Bull. 54, 158 (2009).
[Crossref]

Y. B. Sheng, J. Liu, S. Y. Zhao, and L. Zhou, “Multipartite entanglement concentration for nitrogen-vacancy center and microtoroidal resonator system, ” Chin. Sci. Bull. 59, 3507 (2013).
[Crossref]

Y. Liu and J. X. Cui, “Realization of Kraus operators and POVM measurements using a duality quantum computer,” Chin. Sci. Bull. 59, 2298(2014).
[Crossref]

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

Nature(London). (1)

J. W. Pan, C. Simon, C. Brukner, and A. Zelinger, “Entanglement purification,” Nature(London). 410, 1067 (2001).
[Crossref]

Optics express (1)

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

Phys. Rev. A (14)

M. M. Wilde and D. B. Uskov, “Linear-optical hyperentanglement assisted quantum error-correcting code,” Phys. Rev. A 79, 022305 (2009).
[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. S. Liu, G. L. Long, D. M. Tong, and Feng Li, “General scheme for superdense coding between multiparties,” Phys. Rev. A 65, 022304 (2002).
[Crossref]

M. Hillery and V. Bužek, “Quantum secret sharing,” Phys. Rev. A 59, 1829 (1999).
[Crossref]

L. Xiao, G. L. Long, F.-G. Deng, and J. -W. Pan, “Efficient multiparty quantum-secret-sharing schemes,” Phys. Rev. A 69, 052307 (2004).
[Crossref]

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

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).
[Crossref]

C. Simon and J. W. Pan, “Polarization entanglement purification using spatial entanglement,” Phys. Rev. A 89, 257901 (2002).

M. Horodecki and P. Horodecki, “Reduction criterion of separability and limits for a class of distillation protocols,” Phys. Rev. A 59, 4206 (1999).
[Crossref]

T. J. Wang, Y. Lu, and G. L. Long, “Generation and complete analysis of the hyperentangled Bell state for photons assisted by quantum-dot spins in optical microcavities, ” Phys. Rev. A 86, 042337 (2012).
[Crossref]

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

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

H. K. Lo and S. Popescu, “Concentrating entanglement by local actions: Beyond mean values,” Phys. Rev. A 63, 022301 (2001).
[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]

Phys. Rev. A. (1)

Y. W. Cheong, S. W. Lee, J. Lee, and H. -W. Lee, “Entanglement purification for high-dimensional multipartite systems,” Phys. Rev. A. 76, 042314 (2007).
[Crossref]

Phys. Rev. D (1)

P. M. Pearle, “Hidden-variable example based upon data rejection,” Phys. Rev. D 2, 1418 (1970).
[Crossref]

Phys. Rev. Lett. (11)

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880 (1969).
[Crossref]

A. Miyake and H. J. Briegel, “Distillation of multipartite entanglement by complementary stabilizer measurements,” Phys. Rev. Lett. 95, 220501 (2005).
[Crossref] [PubMed]

W. Dür, H. Aschauer, and H. J. Briegel, “Multiparticle entanglement purification for graph states,” Phys. Rev. Lett. 91, 107903 (2003).
[Crossref] [PubMed]

C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722 (1996).
[Crossref] [PubMed]

D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 77, 2818(1996).
[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 (1992).
[Crossref] [PubMed]

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

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

D. Bruss and C. Macchiavello, “Optimal eavesdropping in cryptography with three-dimensional quantum states,” Phys. Rev. Lett. 88, 127901 (2002).
[Crossref] [PubMed]

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[Crossref] [PubMed]

N. Gisin, S. Pironio, and N. Sangouard, “Proposal for implementing device-independent quantum key distribution based on a heralded qubit amplifier,” Phys. Rev. Lett. 105, 070501 (2010).
[Crossref] [PubMed]

Phys. Rev. X. (1)

A. Cabello and F. Sciarrino, “Loophole-free Bell test based on local precertification of photons presence,” Phys. Rev. X. 2, 021010 (2012).

Rev. Mod. Phys. (2)

H. Buhrman, R. Cleve, S. Massar, and R. de Wolf, “Nonlocality and communication complexity,” Rev. Mod. Phys. 82, 665 (2010).
[Crossref]

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

Sci. Bull. (1)

R. Heilmann, M. Gräfe, S Nolte, and A Szameit, “A novel integrated quantum circuit for high-order W-state generation and its highly precise characterization,” Sci. Bull. 60, 96(2015).
[Crossref]

Sci. China- Phys Mech Astron (1)

C. Wang, L. Y. He, Y. Zhang, H. Q. Ma, and R. Zhang, “Complete entanglement analysis on electron spins using quantum dot and microcavity coupled system, ” Sci. China- Phys Mech Astron 56, 2054 (2013).
[Crossref]

Scientific reports (1)

S. Y. Hou, Y. B. Sheng, G. R. Feng, and G. L. Long, “Experimental Optimal Single Qubit Purification in an NMR Quantum Information Processor,” Scientific reports 4, 6857(2014).
[Crossref] [PubMed]

Other (3)

J. S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge University, 1987).

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).

After the linear optical entanglement purification operation [23] in polarization DOF on the photon-pairs AB and A1B1, the final state of the resived photon-pair A′B′ is ρA′B′=1T1T2[f2+(1−f)2]+(1−T1)T2+(1−T2)T1+(1−T1)(1−T2)(2f+1){(1−T1)(1−T2)(2f+1)2|vac,vac〉A′B′〈vac|+(1−T1)T24|vac〉A′〈vac|⊗[f|H〉B′〈H|+(1−f)|V〉B′〈V|]+T1(1−T2)4|vac〉A′〈vac|⊗[f|V〉B′〈V|+(1−f)|H〉B′〈H|]+(1−T1)T24|vac〉B′〈vac|⊗[f|V〉A′〈V|+(1−f)|H〉A′〈H|]+T1(1−T2)4|vac〉B′〈vac|⊗[f|H〉A′〈H|+(1−f)|V〉A′〈V|]+T1T2[f2+(1−f)2]2[f′|ϕ+〉A′B′〈ϕ++(1−f′)|ψ+〉A′B′〈ψ+||]}, where f′=f2f2+(1−f)2.

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Figures (3)

Fig. 1
Fig. 1

The schematic diagram of the setup for QND parity-check measurement and qubit amplification. The inset shows the structure of detectors D. The setup consists of four input ports (marked with a1, a2, c1, c2), eight auxiliary input ports (marked with b1, b2, b3, b4, e1, e2, e3, e4), four output ports (marked with a′1, a′2, c′1, c′2), two polarizing beam splitters (PBS) which transmit a horizontally polarized photon |H〉 and reflect a vertically polarized photon |V〉. Successful operation of the distilling is heralded by eight-photon coincidence detection on the eight detectors D1, D2, D3, D4, D5, D6, D7 and D8.

Fig. 2
Fig. 2

Fidelity of the hyperentangled photon-pairs in polarization DOF and spatial-mode DOF for the cases with F1 = F2 = f. F’ and F represent the fidelity after and before hyperentanglement purification operation, respectively.

Fig. 3
Fig. 3

Relative weight of the vacuum component of the hyperentangled photon-pairs (Pvac or P′vac) as a function of the transmission coefficient T in the case T1 = T2 = T for different initial real parameters f.

Tables (1)

Tables Icon

Table 1 Relation between the final states of D1D2D3D4(D5D6D7D8) and the corresponding single qubit operations on the photon C′.

Equations (15)

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| ψ 0 AC = [ ( 1 P 1 ) | vac A vac | + P 1 | ψ A ψ A | ] [ ( 1 P 2 ) | vac C vac | + P 2 | ψ C ψ C | ] ,
| ψ A = ( α 1 | a 1 + β 1 | a 2 ) A S ( γ 1 | H + ξ 1 | V ) A P , | ψ C = ( α 2 | c 1 + β 2 | c 2 ) C S ( γ 2 | H + ξ 2 | V ) C P .
| ω = 1 2 [ ( | H V H V + | V H V H ) b 1 b 2 b 3 b 4 ( | H H H H e 1 e 2 e 3 e 4 ) + ( | V V V V ) b 1 b 2 b 3 b 4 ( | H V H V + | V H V H ) e 1 e 2 e 3 e 4 ] ,
| ψ A | ψ C | w PBS 1 , 2 ( α 1 γ 1 | H D 1 + β 1 γ 1 | H D 2 + α 1 ξ 1 | V D 8 + β 1 ξ 1 | V D 7 ) ( α 2 γ 2 | H D 3 + β 2 γ 2 | H D 4 + α 2 ξ 2 | V D 6 + β 2 ξ 2 | V D 5 ) 1 2 [ ( | H a 1 V D 2 H c 1 V D 4 + | V D 1 H a 2 V D 3 H c 2 ) | H D 5 H D 6 H D 7 H D 8 + | V D 1 V D 2 V D 3 V D 4 ( | H D 5 V c 1 H D 7 V a 1 + | V c 2 H D 6 V a 2 H D 8 ) ] .
χ ( α 1 α 2 γ 1 γ 2 | H a 1 H c 1 | H D 1 H D 2 H D 3 V D 4 H D 5 H D 6 H D 7 H D 8 + α 1 α 2 ξ 1 ξ 2 | V a 1 V c 1 | V D 1 V D 2 V D 3 V D 4 H D 5 V D 6 H D 7 V D 8 + β 1 β 2 γ 1 γ 2 | H a 2 H c 2 | V D 1 H D 2 V D 3 H D 4 H D 5 H D 6 H D 7 H D 8 + β 1 β 2 ξ 1 ξ 2 | V a 2 V c 2 | V D 1 V D 2 V D 3 V D 4 V D 5 H D 6 V D 7 H D 8 ) .
1 8 | ψ A C even ( | L D 1 D 2 D 3 D 4 | L D 5 D 6 D 7 D 8 | M D 1 D 2 D 3 D 4 | M D 5 D 6 D 7 D 8 ) + χ 8 [ ( | A + | B | C + | D ) ( | L D 1 D 2 D 3 D 4 | M D 5 D 6 D 7 D 8 | M D 1 D 2 D 3 D 4 | L D 5 D 6 D 7 D 8 ) + ( | A | B + | C | D ) ( | N D 1 D 2 D 3 D 4 | N D 5 D 6 D 7 D 8 | K D 1 D 2 D 3 D 4 | K D 5 D 6 D 7 D 8 ) + ( | A | B | C + | D ) ( | N D 1 D 2 D 3 D 4 | K D 5 D 6 D 7 D 8 | K D 1 D 2 D 3 D 4 | N D 5 D 6 D 7 D 8 ) + ( | A + | B + | C | D ) ( | L D 1 D 2 D 3 D 4 | N D 5 D 6 D 7 D 8 | M D 1 D 2 D 3 D 4 | K D 5 D 6 D 7 D 8 ) + ( | A + | B | C + | D ) ( | L D 1 D 2 D 3 D 4 | K D 5 D 6 D 7 D 8 | M D 1 D 2 D 3 D 4 | N D 5 D 6 D 7 D 8 ) + ( | A | B + | C + | D ) ( | N D 1 D 2 D 3 D 4 | L D 5 D 6 D 7 D 8 | K D 1 D 2 D 3 D 4 | M D 5 D 6 D 7 D 8 ) + ( | A | B | C | D ) ( | N D 1 D 2 D 3 D 4 | M D 5 D 6 D 7 D 8 | K D 1 D 2 D 3 D 4 | L D 5 D 6 D 7 D 8 ) ] ,
| ψ A C even = χ ( α 1 α 2 | a 1 c 1 + β 1 β 2 | a 2 c 2 ) A C ( γ 1 γ 2 | H H + ξ 1 ξ 2 | V V ) A C , | A = α 1 α 2 γ 1 γ 2 | H H A C | a 1 c 1 A C , | B = β 1 β 2 γ 1 γ 2 | H H A C | a 2 c 2 A C , | C = α 1 α 2 ξ 1 ξ 2 | V V A C | a 1 c 1 A C , | D = β 1 β 2 ξ 1 ξ 2 | V V A C | a 2 c 2 A C , | L = 1 2 ( | H H H H + | H V H V + | V H V H + | V V V V ) , | M = 1 2 ( | H H V V + | H V V H + | V H H V + | V V H H ) , | N = 1 2 ( | H H V H + | H V V V + | V H H H + | V V H V ) , | K = 1 2 ( | H H H V + | H V H H + | V H V V + | V V V H ) .
ρ AB = τ 1 [ F 1 | ϕ + P ϕ + | + ( 1 F 1 ) | ψ + P ψ + | ] AB [ F 2 | ϕ + S ϕ + | + ( 1 F 1 ) | ψ + S ψ + | ] AB + τ 2 | + A S + | | + A P + | | vac B vac | + τ 3 | vac A vac | | + B S + | | + B P + | + τ 4 | vac AB vac | ,
ρ CD = τ 1 [ F 1 | ϕ + P ϕ + | + ( 1 F 1 ) | ψ + P ψ + | ] CD [ F 2 | ϕ + S ϕ + | + ( 1 F 2 ) | ψ + S ψ + | ] CD + τ 2 | + C S + | | + C P + | | vac D vac | + τ 3 | vac C vac | | + D S + | | + D P + | + τ 4 | vac CD vac | ,
ρ ABCD = [ F 1 | Φ + P Φ + | + ( 1 F 1 ) | Ψ + P Ψ + | ] ABCD [ F 2 | Φ + S Φ + | + ( 1 F 2 ) | Ψ + S Ψ + | ] ABCD ,
| Φ + ABCD P = 1 2 ( | H H H H + | V V V V ) ABCD , | Ψ + ABCD P = 1 2 ( | H V H V + | V H V H ) ABCD , | Φ + ABCD S = 1 2 ( | a 1 b 1 c 1 d 1 + | a 2 b 2 c 2 d 2 ) ABCD , | Ψ + ABCD S = 1 2 ( | a 1 b 2 c 1 d 2 + | a 2 b 1 c 2 d 1 ) ABCD .
ρ ABCD = 1 16 { [ F 1 | ϕ + P ϕ + | + ( 1 F 1 ) | ψ + P ψ + | ] AB | + + CD P + [ F 1 | ϕ + P ϕ + | ( 1 F 1 ) | ψ + P ψ + | ] AB | CD P + [ F 1 | ϕ P ϕ | + ( 1 F 1 ) | ψ P ψ | ] AB | + CD P + [ F 1 | ϕ P ϕ | ( 1 F 1 ) | ψ P ψ | ] AB | + CD P } { [ F 2 | ϕ + S ϕ + | + ( 1 F 2 ) | ψ + S ψ + | ] AB | + + CD S + [ F 2 | ϕ + S ϕ + | ( 1 F 2 ) | ψ + S ψ + | ] AB | CD S + [ F 2 | ϕ S ϕ | ( 1 F 2 ) | ψ S ψ | ] AB | + CD S + [ F 2 | ϕ S ϕ | ( 1 F 2 ) | ψ S ψ | ] AB | + CD S } ,
| ϕ AB P = 1 2 ( | H H | V V ) A B , | ψ AB P = 1 2 ( | H V | V H ) A B , | ϕ AB S = 1 2 ( | a 1 b 1 | a 2 b 2 ) A B , | ψ AB S = 1 2 ( | a 1 b 2 | a 2 b 1 ) AB .
ρ AB P = T 1 T 2 [ f | ϕ + P ϕ + | + ( 1 f ) | ψ + P ψ + | ] AB + ( 1 T 1 ) T 2 | v a c A v a c | | + B P + | + T 1 ( 1 T 2 ) | + A P + | | v a c B v a c | + ( 1 T 1 ) ( 1 T 2 ) | v a c A v a c | | v a c B v a c | .
ξ = T 1 T 2 [ f 2 + ( 1 f ) 2 ] T 1 T 2 [ f 2 + ( 1 f ) 2 + ( 1 T 1 ) T 2 + ( 1 T 2 ) T 1 + ( 1 T 1 ) ( 1 T 2 ) ( 2 f + 1 ) ] .

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