Abstract

Einstein-Podolsky-Rosen steering is an intermediate relationship between entanglement and Bell nonlocality in the hierarchical structure of quantum nonlocality. To certify the steerability of the entangled state, Mermin steering inequality is supposed to be violated by exceeding the inequality bound of 2. We present an experimental generation of post-selected three-photon entangled states and witness a maximal violation of the inequality up to 3.50±0.05. In the context of observing the maximal violation of Mermin steering inequality which requires measuring on the GHZ state, we derive a tight lower bound on the GHZ-fidelity that can be certified from the Mermin steering inequality violation. From this bound, it follows that the violation of Mermin steering inequality by 3.5 certifies the GHZ-fidelity of 78.66% at least. On the other hand, the above maximal violation of Mermin steering inequality observed in our experimental setup is produced by a post-selected entangled state having the GHZ-fidelity of 87.25 ± 0.34% through quantum tomography.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (2)

A. C. S. Costa, R. Uola, and O. Gühne, “Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems,” Entropy 20, 763 (2018).
[Crossref]

C. Jebaratnam, D. Das, A. Roy, A. Mukherjee, S. S. Bhattacharya, B. Bhattacharya, A. Riccardi, and D. Sarkar, “Tripartite-entanglement detection through tripartite quantum steering in one-sided and two-sided device-independent scenarios,” Phys. Rev. A 98, 022101 (2018).
[Crossref]

2016 (2)

J. Kaniewski, “Analytic and Nearly Optimal Self-Testing Bounds for the Clauser-Horne-Shimony-Holt and Mermin Inequalities,” Phys. Rev. Lett. 117, 070402 (2016).
[Crossref] [PubMed]

I. Šupić and M. J. Hoban, “Self-testing through EPR-steering,” New J. Phys. 18, 075006 (2016).
[Crossref]

2015 (5)

C. Zhang, Y. F. Huang, Z. Wang, B. H. Liu, C. F. Li, and G. C. Guo, “Experimental greenberger-horne-zeilinger-type six-photon quantum nonlocality,” Phys. Rev. Lett. 115, 260402 (2015).
[Crossref]

M. Żukowski, A. Dutta, and Z. Yin, “Geometric Bell-like Inequalities for Steering,” Phys. Rev. A 91, 032107 (2015).
[Crossref]

S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).
[Crossref]

D. Cavalcanti, P. Skrzypczyk, G. Aguilar, R. Nery, P. S. Ribeiro, and S. Walborn, “Detection of entanglement in asymmetric quantum networks and multipartite quantum steering,” Nat. Commun. 6, 7941 (2015).
[Crossref] [PubMed]

I. Kogias, P. Skrzypczyk, D. Cavalcanti, A. Acín, and G. Adesso, “Hierarchy of Steering Criteria Based on Moments for All Bipartite Quantum Systems,” Phys. Rev. Lett. 115, 210401 (2015).
[Crossref] [PubMed]

2014 (3)

N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Publisher’s Note: Bell nonlocality,” Rev. Mod. Phys. 86, 839 (2014).
[Crossref]

T. Pramanik, M. Kaplan, and A. S. Majumdar, “Fine-grained Einstein-Podolsky-Rosen–steering inequalities,” Phys. Rev. A 90, 050305 (2014).
[Crossref]

K. F. Pál, T. Vértesi, and M. Navascués, “Device-independent tomography of multipartite quantum states,” Phys. Rev. A 90, 042340 (2014).
[Crossref]

2013 (4)

Q. Y. He and M. D. Reid, “Genuine Multipartite Einstein-Podolsky-Rosen Steering,” Phys. Rev. Lett. 111, 250403 (2013).
[Crossref]

J. Schneeloch, C. J. Broadbent, S. P. Walborn, E. G. Cavalcanti, and J. C. Howell, “Einstein-Podolsky-Rosen steering inequalities from entropic uncertainty relations,” Phys. Rev. A 87, 062103 (2013).
[Crossref]

J. L. Chen, X. J. Ye, C. F. Wu, H. Y. Su, A. Cabello, L. C. Kwek, and C. H. Oh, “All-Versus-Nothing Proof of Einstein-Podolsky-Rosen Steering,” Sci. Rep. 3, 2143 (2013).
[Crossref] [PubMed]

J. D. Bancal, J. Barrett, N. Gisin, and S. Pironio, “Definitions of multipartite nonlocality,” Phys. Rev. A 88, 014102 (2013).
[Crossref]

2011 (1)

E. G. Cavalcanti, Q. Y. He, M. D. Reid, and H. M. Wiseman, “Unified Criteria for Multipartite Quantum Nonlocality,” Phys. Rev. A 84, 032115 (2011).
[Crossref]

2009 (1)

M. Reid, P. Drummond, W. Bowen, E. G. Cavalcanti, P. K. Lam, H. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727 (2009).
[Crossref]

2008 (1)

A. Cabello, D. Rodrıguez, and I. Villanueva, “Necessary and sufficient detection efficiency for the mermin inequalities,” Phys. Rev. Lett. 101, 120402 (2008).
[Crossref] [PubMed]

2007 (3)

S. J. Jones, H. M. Wiseman, and A. C. Doherty, “Entanglement, Einstein-Podolsky-Rosen correlations, Bell nonlocality, and steering,” Phys. Rev. A 76, 052116 (2007).
[Crossref]

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1, 165–171 (2007).
[Crossref]

H. M. Wiseman, S. J. Jones, and A. C. Doherty, “Steering, Entanglement, Nonlocality, and the Einstein-Podolsky-Rosen Paradox,” Phys. Rev. Lett. 98, 140402 (2007).
[Crossref] [PubMed]

2004 (1)

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[Crossref] [PubMed]

2002 (3)

D. Collins, N. Gisin, S. Popescu, D. Roberts, and V. Scarani, “Bell-Type Inequalities to Detect True n-Body Nonseparability,” Phys. Rev. Lett. 88, 170405 (2002).
[Crossref] [PubMed]

M. Seevinck and G. Svetlichny, “Bell-Type Inequalities for Partial Separability in n-Particle Systems and Quantum Mechanical Violations,” Phys. Rev. Lett. 89, 060401 (2002).
[Crossref] [PubMed]

M. A. Nielsen and I. Chuang, “Quantum Computation and Quantum Information,” Am. J. Phys. 70, 558–559 (2002).
[Crossref]

2001 (2)

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
[Crossref]

M. Seevinck and J. Uffink, “Sufficient conditions for three-particle entanglement and their tests in recent experiments,” Phys. Rev. A 65, 012107 (2001).
[Crossref]

2000 (1)

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

1990 (1)

N. D. Mermin, “Extreme quantum entanglement in a superposition of macroscopically distinct states,” Phys. Rev. Lett. 65, 1838 (1990).
[Crossref] [PubMed]

1964 (1)

J. S. Bell, “On the einstein podolsky rosen paradox,” Physics 1, 195 (1964).
[Crossref]

Acín, A.

I. Kogias, P. Skrzypczyk, D. Cavalcanti, A. Acín, and G. Adesso, “Hierarchy of Steering Criteria Based on Moments for All Bipartite Quantum Systems,” Phys. Rev. Lett. 115, 210401 (2015).
[Crossref] [PubMed]

Adesso, G.

I. Kogias, P. Skrzypczyk, D. Cavalcanti, A. Acín, and G. Adesso, “Hierarchy of Steering Criteria Based on Moments for All Bipartite Quantum Systems,” Phys. Rev. Lett. 115, 210401 (2015).
[Crossref] [PubMed]

Aguilar, G.

D. Cavalcanti, P. Skrzypczyk, G. Aguilar, R. Nery, P. S. Ribeiro, and S. Walborn, “Detection of entanglement in asymmetric quantum networks and multipartite quantum steering,” Nat. Commun. 6, 7941 (2015).
[Crossref] [PubMed]

Andersen, U. L.

M. Reid, P. Drummond, W. Bowen, E. G. Cavalcanti, P. K. Lam, H. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727 (2009).
[Crossref]

Armstrong, S.

S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).
[Crossref]

Bachor, H.

M. Reid, P. Drummond, W. Bowen, E. G. Cavalcanti, P. K. Lam, H. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727 (2009).
[Crossref]

Bachor, H. A.

S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).
[Crossref]

Bancal, J. D.

J. D. Bancal, J. Barrett, N. Gisin, and S. Pironio, “Definitions of multipartite nonlocality,” Phys. Rev. A 88, 014102 (2013).
[Crossref]

Barrett, J.

J. D. Bancal, J. Barrett, N. Gisin, and S. Pironio, “Definitions of multipartite nonlocality,” Phys. Rev. A 88, 014102 (2013).
[Crossref]

Bell, J. S.

J. S. Bell, “On the einstein podolsky rosen paradox,” Physics 1, 195 (1964).
[Crossref]

Bhattacharya, B.

C. Jebaratnam, D. Das, A. Roy, A. Mukherjee, S. S. Bhattacharya, B. Bhattacharya, A. Riccardi, and D. Sarkar, “Tripartite-entanglement detection through tripartite quantum steering in one-sided and two-sided device-independent scenarios,” Phys. Rev. A 98, 022101 (2018).
[Crossref]

Bhattacharya, S. S.

C. Jebaratnam, D. Das, A. Roy, A. Mukherjee, S. S. Bhattacharya, B. Bhattacharya, A. Riccardi, and D. Sarkar, “Tripartite-entanglement detection through tripartite quantum steering in one-sided and two-sided device-independent scenarios,” Phys. Rev. A 98, 022101 (2018).
[Crossref]

Bourennane, M.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[Crossref] [PubMed]

Bouwmeester, D.

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

Bowen, W.

M. Reid, P. Drummond, W. Bowen, E. G. Cavalcanti, P. K. Lam, H. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727 (2009).
[Crossref]

Broadbent, C. J.

J. Schneeloch, C. J. Broadbent, S. P. Walborn, E. G. Cavalcanti, and J. C. Howell, “Einstein-Podolsky-Rosen steering inequalities from entropic uncertainty relations,” Phys. Rev. A 87, 062103 (2013).
[Crossref]

Brunner, N.

N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Publisher’s Note: Bell nonlocality,” Rev. Mod. Phys. 86, 839 (2014).
[Crossref]

Bruß, D.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[Crossref] [PubMed]

Cabello, A.

J. L. Chen, X. J. Ye, C. F. Wu, H. Y. Su, A. Cabello, L. C. Kwek, and C. H. Oh, “All-Versus-Nothing Proof of Einstein-Podolsky-Rosen Steering,” Sci. Rep. 3, 2143 (2013).
[Crossref] [PubMed]

A. Cabello, D. Rodrıguez, and I. Villanueva, “Necessary and sufficient detection efficiency for the mermin inequalities,” Phys. Rev. Lett. 101, 120402 (2008).
[Crossref] [PubMed]

Cavalcanti, D.

I. Kogias, P. Skrzypczyk, D. Cavalcanti, A. Acín, and G. Adesso, “Hierarchy of Steering Criteria Based on Moments for All Bipartite Quantum Systems,” Phys. Rev. Lett. 115, 210401 (2015).
[Crossref] [PubMed]

D. Cavalcanti, P. Skrzypczyk, G. Aguilar, R. Nery, P. S. Ribeiro, and S. Walborn, “Detection of entanglement in asymmetric quantum networks and multipartite quantum steering,” Nat. Commun. 6, 7941 (2015).
[Crossref] [PubMed]

N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Publisher’s Note: Bell nonlocality,” Rev. Mod. Phys. 86, 839 (2014).
[Crossref]

Cavalcanti, E. G.

J. Schneeloch, C. J. Broadbent, S. P. Walborn, E. G. Cavalcanti, and J. C. Howell, “Einstein-Podolsky-Rosen steering inequalities from entropic uncertainty relations,” Phys. Rev. A 87, 062103 (2013).
[Crossref]

E. G. Cavalcanti, Q. Y. He, M. D. Reid, and H. M. Wiseman, “Unified Criteria for Multipartite Quantum Nonlocality,” Phys. Rev. A 84, 032115 (2011).
[Crossref]

M. Reid, P. Drummond, W. Bowen, E. G. Cavalcanti, P. K. Lam, H. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727 (2009).
[Crossref]

Chen, J. L.

J. L. Chen, X. J. Ye, C. F. Wu, H. Y. Su, A. Cabello, L. C. Kwek, and C. H. Oh, “All-Versus-Nothing Proof of Einstein-Podolsky-Rosen Steering,” Sci. Rep. 3, 2143 (2013).
[Crossref] [PubMed]

Chuang, I.

M. A. Nielsen and I. Chuang, “Quantum Computation and Quantum Information,” Am. J. Phys. 70, 558–559 (2002).
[Crossref]

Collins, D.

D. Collins, N. Gisin, S. Popescu, D. Roberts, and V. Scarani, “Bell-Type Inequalities to Detect True n-Body Nonseparability,” Phys. Rev. Lett. 88, 170405 (2002).
[Crossref] [PubMed]

Costa, A. C. S.

A. C. S. Costa, R. Uola, and O. Gühne, “Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems,” Entropy 20, 763 (2018).
[Crossref]

Daniell, M.

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

Das, D.

C. Jebaratnam, D. Das, A. Roy, A. Mukherjee, S. S. Bhattacharya, B. Bhattacharya, A. Riccardi, and D. Sarkar, “Tripartite-entanglement detection through tripartite quantum steering in one-sided and two-sided device-independent scenarios,” Phys. Rev. A 98, 022101 (2018).
[Crossref]

Doherty, A. C.

H. M. Wiseman, S. J. Jones, and A. C. Doherty, “Steering, Entanglement, Nonlocality, and the Einstein-Podolsky-Rosen Paradox,” Phys. Rev. Lett. 98, 140402 (2007).
[Crossref] [PubMed]

S. J. Jones, H. M. Wiseman, and A. C. Doherty, “Entanglement, Einstein-Podolsky-Rosen correlations, Bell nonlocality, and steering,” Phys. Rev. A 76, 052116 (2007).
[Crossref]

Drummond, P.

M. Reid, P. Drummond, W. Bowen, E. G. Cavalcanti, P. K. Lam, H. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727 (2009).
[Crossref]

Dutta, A.

M. Żukowski, A. Dutta, and Z. Yin, “Geometric Bell-like Inequalities for Steering,” Phys. Rev. A 91, 032107 (2015).
[Crossref]

Eibl, M.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[Crossref] [PubMed]

Gaertner, S.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[Crossref] [PubMed]

Gisin, N.

J. D. Bancal, J. Barrett, N. Gisin, and S. Pironio, “Definitions of multipartite nonlocality,” Phys. Rev. A 88, 014102 (2013).
[Crossref]

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1, 165–171 (2007).
[Crossref]

D. Collins, N. Gisin, S. Popescu, D. Roberts, and V. Scarani, “Bell-Type Inequalities to Detect True n-Body Nonseparability,” Phys. Rev. Lett. 88, 170405 (2002).
[Crossref] [PubMed]

Gong, Q.

S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).
[Crossref]

Greenberger, D. M.

D. M. Greenberger, M. A. Horne, and A. Zeilinger, “Going beyond Bell’s theorem,” in Bell’s Theorem, Quantum Theory and Conceptions of the Universe, M. Kaftos, ed. (Kluwer Academic, 1989).
[Crossref]

Gühne, O.

A. C. S. Costa, R. Uola, and O. Gühne, “Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems,” Entropy 20, 763 (2018).
[Crossref]

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[Crossref] [PubMed]

Guo, G. C.

C. Zhang, Y. F. Huang, Z. Wang, B. H. Liu, C. F. Li, and G. C. Guo, “Experimental greenberger-horne-zeilinger-type six-photon quantum nonlocality,” Phys. Rev. Lett. 115, 260402 (2015).
[Crossref]

He, Q.

S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).
[Crossref]

He, Q. Y.

Q. Y. He and M. D. Reid, “Genuine Multipartite Einstein-Podolsky-Rosen Steering,” Phys. Rev. Lett. 111, 250403 (2013).
[Crossref]

E. G. Cavalcanti, Q. Y. He, M. D. Reid, and H. M. Wiseman, “Unified Criteria for Multipartite Quantum Nonlocality,” Phys. Rev. A 84, 032115 (2011).
[Crossref]

Hoban, M. J.

I. Šupić and M. J. Hoban, “Self-testing through EPR-steering,” New J. Phys. 18, 075006 (2016).
[Crossref]

Horne, M. A.

D. M. Greenberger, M. A. Horne, and A. Zeilinger, “Going beyond Bell’s theorem,” in Bell’s Theorem, Quantum Theory and Conceptions of the Universe, M. Kaftos, ed. (Kluwer Academic, 1989).
[Crossref]

Howell, J. C.

J. Schneeloch, C. J. Broadbent, S. P. Walborn, E. G. Cavalcanti, and J. C. Howell, “Einstein-Podolsky-Rosen steering inequalities from entropic uncertainty relations,” Phys. Rev. A 87, 062103 (2013).
[Crossref]

Huang, Y. F.

C. Zhang, Y. F. Huang, Z. Wang, B. H. Liu, C. F. Li, and G. C. Guo, “Experimental greenberger-horne-zeilinger-type six-photon quantum nonlocality,” Phys. Rev. Lett. 115, 260402 (2015).
[Crossref]

Hyllus, P.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[Crossref] [PubMed]

James, D. F. V.

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
[Crossref]

Janousek, J.

S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).
[Crossref]

Jebaratnam, C.

C. Jebaratnam, D. Das, A. Roy, A. Mukherjee, S. S. Bhattacharya, B. Bhattacharya, A. Riccardi, and D. Sarkar, “Tripartite-entanglement detection through tripartite quantum steering in one-sided and two-sided device-independent scenarios,” Phys. Rev. A 98, 022101 (2018).
[Crossref]

Jones, S. J.

H. M. Wiseman, S. J. Jones, and A. C. Doherty, “Steering, Entanglement, Nonlocality, and the Einstein-Podolsky-Rosen Paradox,” Phys. Rev. Lett. 98, 140402 (2007).
[Crossref] [PubMed]

S. J. Jones, H. M. Wiseman, and A. C. Doherty, “Entanglement, Einstein-Podolsky-Rosen correlations, Bell nonlocality, and steering,” Phys. Rev. A 76, 052116 (2007).
[Crossref]

Kaniewski, J.

J. Kaniewski, “Analytic and Nearly Optimal Self-Testing Bounds for the Clauser-Horne-Shimony-Holt and Mermin Inequalities,” Phys. Rev. Lett. 117, 070402 (2016).
[Crossref] [PubMed]

J. Kaniewski, Private communication.

Kaplan, M.

T. Pramanik, M. Kaplan, and A. S. Majumdar, “Fine-grained Einstein-Podolsky-Rosen–steering inequalities,” Phys. Rev. A 90, 050305 (2014).
[Crossref]

Kogias, I.

I. Kogias, P. Skrzypczyk, D. Cavalcanti, A. Acín, and G. Adesso, “Hierarchy of Steering Criteria Based on Moments for All Bipartite Quantum Systems,” Phys. Rev. Lett. 115, 210401 (2015).
[Crossref] [PubMed]

Kurtsiefer, C.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[Crossref] [PubMed]

Kwek, L. C.

J. L. Chen, X. J. Ye, C. F. Wu, H. Y. Su, A. Cabello, L. C. Kwek, and C. H. Oh, “All-Versus-Nothing Proof of Einstein-Podolsky-Rosen Steering,” Sci. Rep. 3, 2143 (2013).
[Crossref] [PubMed]

Kwiat, P. G.

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
[Crossref]

Lam, P. K.

S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).
[Crossref]

M. Reid, P. Drummond, W. Bowen, E. G. Cavalcanti, P. K. Lam, H. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727 (2009).
[Crossref]

Leuchs, G.

M. Reid, P. Drummond, W. Bowen, E. G. Cavalcanti, P. K. Lam, H. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727 (2009).
[Crossref]

Lewenstein, M.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[Crossref] [PubMed]

Li, C. F.

C. Zhang, Y. F. Huang, Z. Wang, B. H. Liu, C. F. Li, and G. C. Guo, “Experimental greenberger-horne-zeilinger-type six-photon quantum nonlocality,” Phys. Rev. Lett. 115, 260402 (2015).
[Crossref]

Liu, B. H.

C. Zhang, Y. F. Huang, Z. Wang, B. H. Liu, C. F. Li, and G. C. Guo, “Experimental greenberger-horne-zeilinger-type six-photon quantum nonlocality,” Phys. Rev. Lett. 115, 260402 (2015).
[Crossref]

Majumdar, A. S.

T. Pramanik, M. Kaplan, and A. S. Majumdar, “Fine-grained Einstein-Podolsky-Rosen–steering inequalities,” Phys. Rev. A 90, 050305 (2014).
[Crossref]

Mermin, N. D.

N. D. Mermin, “Extreme quantum entanglement in a superposition of macroscopically distinct states,” Phys. Rev. Lett. 65, 1838 (1990).
[Crossref] [PubMed]

Mukherjee, A.

C. Jebaratnam, D. Das, A. Roy, A. Mukherjee, S. S. Bhattacharya, B. Bhattacharya, A. Riccardi, and D. Sarkar, “Tripartite-entanglement detection through tripartite quantum steering in one-sided and two-sided device-independent scenarios,” Phys. Rev. A 98, 022101 (2018).
[Crossref]

Munro, W. J.

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
[Crossref]

Navascués, M.

K. F. Pál, T. Vértesi, and M. Navascués, “Device-independent tomography of multipartite quantum states,” Phys. Rev. A 90, 042340 (2014).
[Crossref]

Nery, R.

D. Cavalcanti, P. Skrzypczyk, G. Aguilar, R. Nery, P. S. Ribeiro, and S. Walborn, “Detection of entanglement in asymmetric quantum networks and multipartite quantum steering,” Nat. Commun. 6, 7941 (2015).
[Crossref] [PubMed]

Nielsen, M. A.

M. A. Nielsen and I. Chuang, “Quantum Computation and Quantum Information,” Am. J. Phys. 70, 558–559 (2002).
[Crossref]

Oh, C. H.

J. L. Chen, X. J. Ye, C. F. Wu, H. Y. Su, A. Cabello, L. C. Kwek, and C. H. Oh, “All-Versus-Nothing Proof of Einstein-Podolsky-Rosen Steering,” Sci. Rep. 3, 2143 (2013).
[Crossref] [PubMed]

Pál, K. F.

K. F. Pál, T. Vértesi, and M. Navascués, “Device-independent tomography of multipartite quantum states,” Phys. Rev. A 90, 042340 (2014).
[Crossref]

Pan, J. W.

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

Pironio, S.

N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Publisher’s Note: Bell nonlocality,” Rev. Mod. Phys. 86, 839 (2014).
[Crossref]

J. D. Bancal, J. Barrett, N. Gisin, and S. Pironio, “Definitions of multipartite nonlocality,” Phys. Rev. A 88, 014102 (2013).
[Crossref]

Popescu, S.

D. Collins, N. Gisin, S. Popescu, D. Roberts, and V. Scarani, “Bell-Type Inequalities to Detect True n-Body Nonseparability,” Phys. Rev. Lett. 88, 170405 (2002).
[Crossref] [PubMed]

Pramanik, T.

T. Pramanik, M. Kaplan, and A. S. Majumdar, “Fine-grained Einstein-Podolsky-Rosen–steering inequalities,” Phys. Rev. A 90, 050305 (2014).
[Crossref]

Reid, M.

M. Reid, P. Drummond, W. Bowen, E. G. Cavalcanti, P. K. Lam, H. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727 (2009).
[Crossref]

Reid, M. D.

S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).
[Crossref]

Q. Y. He and M. D. Reid, “Genuine Multipartite Einstein-Podolsky-Rosen Steering,” Phys. Rev. Lett. 111, 250403 (2013).
[Crossref]

E. G. Cavalcanti, Q. Y. He, M. D. Reid, and H. M. Wiseman, “Unified Criteria for Multipartite Quantum Nonlocality,” Phys. Rev. A 84, 032115 (2011).
[Crossref]

Ribeiro, P. S.

D. Cavalcanti, P. Skrzypczyk, G. Aguilar, R. Nery, P. S. Ribeiro, and S. Walborn, “Detection of entanglement in asymmetric quantum networks and multipartite quantum steering,” Nat. Commun. 6, 7941 (2015).
[Crossref] [PubMed]

Riccardi, A.

C. Jebaratnam, D. Das, A. Roy, A. Mukherjee, S. S. Bhattacharya, B. Bhattacharya, A. Riccardi, and D. Sarkar, “Tripartite-entanglement detection through tripartite quantum steering in one-sided and two-sided device-independent scenarios,” Phys. Rev. A 98, 022101 (2018).
[Crossref]

Roberts, D.

D. Collins, N. Gisin, S. Popescu, D. Roberts, and V. Scarani, “Bell-Type Inequalities to Detect True n-Body Nonseparability,” Phys. Rev. Lett. 88, 170405 (2002).
[Crossref] [PubMed]

Rodriguez, D.

A. Cabello, D. Rodrıguez, and I. Villanueva, “Necessary and sufficient detection efficiency for the mermin inequalities,” Phys. Rev. Lett. 101, 120402 (2008).
[Crossref] [PubMed]

Roy, A.

C. Jebaratnam, D. Das, A. Roy, A. Mukherjee, S. S. Bhattacharya, B. Bhattacharya, A. Riccardi, and D. Sarkar, “Tripartite-entanglement detection through tripartite quantum steering in one-sided and two-sided device-independent scenarios,” Phys. Rev. A 98, 022101 (2018).
[Crossref]

Sanpera, A.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[Crossref] [PubMed]

Sarkar, D.

C. Jebaratnam, D. Das, A. Roy, A. Mukherjee, S. S. Bhattacharya, B. Bhattacharya, A. Riccardi, and D. Sarkar, “Tripartite-entanglement detection through tripartite quantum steering in one-sided and two-sided device-independent scenarios,” Phys. Rev. A 98, 022101 (2018).
[Crossref]

Scarani, V.

N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Publisher’s Note: Bell nonlocality,” Rev. Mod. Phys. 86, 839 (2014).
[Crossref]

D. Collins, N. Gisin, S. Popescu, D. Roberts, and V. Scarani, “Bell-Type Inequalities to Detect True n-Body Nonseparability,” Phys. Rev. Lett. 88, 170405 (2002).
[Crossref] [PubMed]

Schneeloch, J.

J. Schneeloch, C. J. Broadbent, S. P. Walborn, E. G. Cavalcanti, and J. C. Howell, “Einstein-Podolsky-Rosen steering inequalities from entropic uncertainty relations,” Phys. Rev. A 87, 062103 (2013).
[Crossref]

Seevinck, M.

M. Seevinck and G. Svetlichny, “Bell-Type Inequalities for Partial Separability in n-Particle Systems and Quantum Mechanical Violations,” Phys. Rev. Lett. 89, 060401 (2002).
[Crossref] [PubMed]

M. Seevinck and J. Uffink, “Sufficient conditions for three-particle entanglement and their tests in recent experiments,” Phys. Rev. A 65, 012107 (2001).
[Crossref]

Skrzypczyk, P.

I. Kogias, P. Skrzypczyk, D. Cavalcanti, A. Acín, and G. Adesso, “Hierarchy of Steering Criteria Based on Moments for All Bipartite Quantum Systems,” Phys. Rev. Lett. 115, 210401 (2015).
[Crossref] [PubMed]

D. Cavalcanti, P. Skrzypczyk, G. Aguilar, R. Nery, P. S. Ribeiro, and S. Walborn, “Detection of entanglement in asymmetric quantum networks and multipartite quantum steering,” Nat. Commun. 6, 7941 (2015).
[Crossref] [PubMed]

Su, H. Y.

J. L. Chen, X. J. Ye, C. F. Wu, H. Y. Su, A. Cabello, L. C. Kwek, and C. H. Oh, “All-Versus-Nothing Proof of Einstein-Podolsky-Rosen Steering,” Sci. Rep. 3, 2143 (2013).
[Crossref] [PubMed]

Šupic, I.

I. Šupić and M. J. Hoban, “Self-testing through EPR-steering,” New J. Phys. 18, 075006 (2016).
[Crossref]

Svetlichny, G.

M. Seevinck and G. Svetlichny, “Bell-Type Inequalities for Partial Separability in n-Particle Systems and Quantum Mechanical Violations,” Phys. Rev. Lett. 89, 060401 (2002).
[Crossref] [PubMed]

Teh, R. Y.

S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).
[Crossref]

Thew, R.

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1, 165–171 (2007).
[Crossref]

Uffink, J.

M. Seevinck and J. Uffink, “Sufficient conditions for three-particle entanglement and their tests in recent experiments,” Phys. Rev. A 65, 012107 (2001).
[Crossref]

Uola, R.

A. C. S. Costa, R. Uola, and O. Gühne, “Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems,” Entropy 20, 763 (2018).
[Crossref]

Vértesi, T.

K. F. Pál, T. Vértesi, and M. Navascués, “Device-independent tomography of multipartite quantum states,” Phys. Rev. A 90, 042340 (2014).
[Crossref]

Villanueva, I.

A. Cabello, D. Rodrıguez, and I. Villanueva, “Necessary and sufficient detection efficiency for the mermin inequalities,” Phys. Rev. Lett. 101, 120402 (2008).
[Crossref] [PubMed]

Walborn, S.

D. Cavalcanti, P. Skrzypczyk, G. Aguilar, R. Nery, P. S. Ribeiro, and S. Walborn, “Detection of entanglement in asymmetric quantum networks and multipartite quantum steering,” Nat. Commun. 6, 7941 (2015).
[Crossref] [PubMed]

Walborn, S. P.

J. Schneeloch, C. J. Broadbent, S. P. Walborn, E. G. Cavalcanti, and J. C. Howell, “Einstein-Podolsky-Rosen steering inequalities from entropic uncertainty relations,” Phys. Rev. A 87, 062103 (2013).
[Crossref]

Wang, M.

S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).
[Crossref]

Wang, Z.

C. Zhang, Y. F. Huang, Z. Wang, B. H. Liu, C. F. Li, and G. C. Guo, “Experimental greenberger-horne-zeilinger-type six-photon quantum nonlocality,” Phys. Rev. Lett. 115, 260402 (2015).
[Crossref]

Wehner, S.

N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Publisher’s Note: Bell nonlocality,” Rev. Mod. Phys. 86, 839 (2014).
[Crossref]

Weinfurter, H.

M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Phys. Rev. Lett. 92, 087902 (2004).
[Crossref] [PubMed]

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

White, A. G.

D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001).
[Crossref]

Wiseman, H. M.

E. G. Cavalcanti, Q. Y. He, M. D. Reid, and H. M. Wiseman, “Unified Criteria for Multipartite Quantum Nonlocality,” Phys. Rev. A 84, 032115 (2011).
[Crossref]

H. M. Wiseman, S. J. Jones, and A. C. Doherty, “Steering, Entanglement, Nonlocality, and the Einstein-Podolsky-Rosen Paradox,” Phys. Rev. Lett. 98, 140402 (2007).
[Crossref] [PubMed]

S. J. Jones, H. M. Wiseman, and A. C. Doherty, “Entanglement, Einstein-Podolsky-Rosen correlations, Bell nonlocality, and steering,” Phys. Rev. A 76, 052116 (2007).
[Crossref]

Wu, C. F.

J. L. Chen, X. J. Ye, C. F. Wu, H. Y. Su, A. Cabello, L. C. Kwek, and C. H. Oh, “All-Versus-Nothing Proof of Einstein-Podolsky-Rosen Steering,” Sci. Rep. 3, 2143 (2013).
[Crossref] [PubMed]

Ye, X. J.

J. L. Chen, X. J. Ye, C. F. Wu, H. Y. Su, A. Cabello, L. C. Kwek, and C. H. Oh, “All-Versus-Nothing Proof of Einstein-Podolsky-Rosen Steering,” Sci. Rep. 3, 2143 (2013).
[Crossref] [PubMed]

Yin, Z.

M. Żukowski, A. Dutta, and Z. Yin, “Geometric Bell-like Inequalities for Steering,” Phys. Rev. A 91, 032107 (2015).
[Crossref]

Zeilinger, A.

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

D. M. Greenberger, M. A. Horne, and A. Zeilinger, “Going beyond Bell’s theorem,” in Bell’s Theorem, Quantum Theory and Conceptions of the Universe, M. Kaftos, ed. (Kluwer Academic, 1989).
[Crossref]

Zhang, C.

C. Zhang, Y. F. Huang, Z. Wang, B. H. Liu, C. F. Li, and G. C. Guo, “Experimental greenberger-horne-zeilinger-type six-photon quantum nonlocality,” Phys. Rev. Lett. 115, 260402 (2015).
[Crossref]

Zukowski, M.

M. Żukowski, A. Dutta, and Z. Yin, “Geometric Bell-like Inequalities for Steering,” Phys. Rev. A 91, 032107 (2015).
[Crossref]

Am. J. Phys. (1)

M. A. Nielsen and I. Chuang, “Quantum Computation and Quantum Information,” Am. J. Phys. 70, 558–559 (2002).
[Crossref]

Entropy (1)

A. C. S. Costa, R. Uola, and O. Gühne, “Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems,” Entropy 20, 763 (2018).
[Crossref]

Nat. (1)

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

Nat. Commun. (1)

D. Cavalcanti, P. Skrzypczyk, G. Aguilar, R. Nery, P. S. Ribeiro, and S. Walborn, “Detection of entanglement in asymmetric quantum networks and multipartite quantum steering,” Nat. Commun. 6, 7941 (2015).
[Crossref] [PubMed]

Nat. Photonics (1)

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1, 165–171 (2007).
[Crossref]

Nat. Phys. (1)

S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein–Podolsky–Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167–172 (2015).
[Crossref]

New J. Phys. (1)

I. Šupić and M. J. Hoban, “Self-testing through EPR-steering,” New J. Phys. 18, 075006 (2016).
[Crossref]

Phys. Rev. A (10)

M. Seevinck and J. Uffink, “Sufficient conditions for three-particle entanglement and their tests in recent experiments,” Phys. Rev. A 65, 012107 (2001).
[Crossref]

K. F. Pál, T. Vértesi, and M. Navascués, “Device-independent tomography of multipartite quantum states,” Phys. Rev. A 90, 042340 (2014).
[Crossref]

J. Schneeloch, C. J. Broadbent, S. P. Walborn, E. G. Cavalcanti, and J. C. Howell, “Einstein-Podolsky-Rosen steering inequalities from entropic uncertainty relations,” Phys. Rev. A 87, 062103 (2013).
[Crossref]

S. J. Jones, H. M. Wiseman, and A. C. Doherty, “Entanglement, Einstein-Podolsky-Rosen correlations, Bell nonlocality, and steering,” Phys. Rev. A 76, 052116 (2007).
[Crossref]

T. Pramanik, M. Kaplan, and A. S. Majumdar, “Fine-grained Einstein-Podolsky-Rosen–steering inequalities,” Phys. Rev. A 90, 050305 (2014).
[Crossref]

M. Żukowski, A. Dutta, and Z. Yin, “Geometric Bell-like Inequalities for Steering,” Phys. Rev. A 91, 032107 (2015).
[Crossref]

E. G. Cavalcanti, Q. Y. He, M. D. Reid, and H. M. Wiseman, “Unified Criteria for Multipartite Quantum Nonlocality,” Phys. Rev. A 84, 032115 (2011).
[Crossref]

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Physics (1)

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Figures (3)

Fig. 1
Fig. 1 Experimental setup for verifying the violation of Mermin steering inequality. It consists of two consecutive spontaneous parametric down-conversion (SPDC) sources. I-BBO: a β-barium borate (BBO) crystal cut for collinear type-I phase-matching; II-BBO: a BBO crystal cut for collinear type-II phase-matching; C-BBO: sandwich-type BBO+HWP+BBO combination; QWP: quarter-wave plate; HWP: half-wave plate; PBS: polarzing beam-splitter; IF2: interference filter with a full width at half maximum (FWHM) of 2 nm and central wavelength of 780 nm; IF3: interference filter with a FWHM of 3 nm and central wavelength of 780 nm; APD: single-photon detector.
Fig. 2
Fig. 2 Quantum state tomography. Real (a) and imaginary (b) parts of the reconstructed density matrix of our GHZ state. The fidelity of our state compared with the ideal one is 87.25 ± 0.34 %.
Fig. 3
Fig. 3 Fig. 3 shows that different parameter of the Mermin steering inequality for states of Eq. (5) with different θ. θ represents the parameter of amplitudes of the state and can be varied with the rotation of the HWP1. The blue circles marked as ’Exp’ denote experimental data for Mermin parameters with error bars. The red curve marked as ’Theo’ represents theoretical predictions. EPR steering exists during θ ∈ (9.2°, 22.5°).

Tables (1)

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Table 1 Four-fold Coincidence of the GHZ State under 32 Basis during 300 Seconds

Equations (10)

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A 0 B 0 C 1 + A 0 B 1 C 0 + A 1 B 0 C 0 A 1 B 1 C 1 LHV 2 ,
F GHZ = max Λ A , Λ B , Λ C ψ GHZ | ( Λ A Λ B Λ C ) ρ ABC | ψ GHZ ,
F GHZ 1 2 + 1 2 γ 2 2 4 2 2 .
p ( a b c | A x B y C z ) = λ p λ P λ ( a | A x ) P λ ( b | B y ) P ( c | C z , ρ C λ ) ,
| A 0 B 0 C 1 + A 0 B 1 C 0 + A 1 B 0 C 0 A 1 B 1 C 1 ? × ? × 2 | LHV LHS 2 ,
F GHZ 2 SDI = max λ A , λ B ψ GHZ | ( λ A λ B 𝟙 ) ρ ABC | ψ GHZ ,
F GHZ 2 SDI 1 2 + 1 2 γ 2 2 4 2 2 ,
| GHZ = ( | H A H B H C i | V A V B V C ) / 2 ,
| GHZ = 1 2 ( cos 2 θ | H A H B H C i sin 2 θ | V A V B V C ) ,
| σ y A σ y B σ y C σ y A σ x B σ x C σ x A σ y B σ x C σ x A σ x B σ y C A B C | 2 .

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