Abstract

Contextuality is a phenomenon at the heart of the quantum mechanical departure from classical behavior, and has been recently identified as a resource in quantum computation. Experimental demonstration of contextuality is thus an important goal. The traditional form of contextuality—as violation of a Kochen–Specker inequality—requires a quantum system with at least three levels, and the status of the assumption of determinism used in deriving those inequalities has been controversial. By considering “unsharp” observables, Liang, Spekkens, and Wiseman (LSW) derived an inequality for generalized noncontextual models that does not assume determinism, and applies already to a qubit. We experimentally implement the LSW test using the polarization states of a heralded single photon and three unsharp binary measurements. We violate the LSW inequality by more than 16 standard deviations, thus showing that our results cannot be reproduced by a noncontextual subset of quantum theory.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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  1. J. S. Bell, “On the Einstein Podolsky Rosen paradox,” Physics 1, 195–200 (1964).
  2. S. Kochen and E. Specker, “The problem of hidden variables in quantum mechanics,” J. Math. Mech. 17, 59–87 (1967).
    [Crossref]
  3. G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of Bell’s inequality under strict Einstein locality conditions,” Phys. Rev. Lett. 81, 5039–5043 (1998).
    [Crossref]
  4. Y.-F. Huang, C.-F. Li, Y.-S. Zhang, J.-W. Pan, and G.-C. Guo, “Experimental test of the Kochen-Specker theorem with single photons,” Phys. Rev. Lett. 90, 250401 (2003).
    [Crossref]
  5. G. Kirchmair, F. Zähringer, R. Gerritsma, M. Kleinmann, O. Gühne, A. Cabello, R. Blatt, and C. F. Roos, “State-independent experimental test of quantum contextuality,” Nature 460, 494–497 (2009).
    [Crossref]
  6. E. Amselem, M. Rådmark, M. Bourennane, and A. Cabello, “State-independent quantum contextuality with single photons,” Phys. Rev. Lett. 103, 160405 (2009).
    [Crossref]
  7. H. Bartosik, J. Klepp, C. Schmitzer, S. Sponar, A. Cabello, H. Rauch, and Y. Hasegawa, “Experimental test of quantum contextuality in neutron interferometry,” Phys. Rev. Lett. 103, 040403 (2009).
    [Crossref]
  8. O. Moussa, C. A. Ryan, D. G. Cory, and R. Laflamme, “Testing contextuality on quantum ensembles with one clean qubit,” Phys. Rev. Lett. 104, 160501 (2010).
    [Crossref]
  9. R. Lapkiewicz, P. Li, C. Schaeff, N. K. Langford, S. Ramelow, M. Wieśniak, and A. Zeilinger, “Experimental non-classicality of an indivisible quantum system,” Nature 474, 490–493 (2011).
    [Crossref]
  10. A. A. Klyachko, M. A. Can, S. Binicioğlu, and A. S. Shumovsky, “Simple test for hidden variables in spin-1 systems,” Phys. Rev. Lett. 101, 020403 (2008).
    [Crossref]
  11. A. Peres, “Two simple proofs of the Kochen-Specker theorem,” J. Phys. A 24, L175 (1991).
    [Crossref]
  12. J. Bub, “Schütte’s tautology and the Kochen-Specker theorem,” Found. Phys. 26, 787–806 (1996).
    [Crossref]
  13. P. Badziag, I. Bengtsson, A. Cabello, and I. Pitowsky, “Universality of state-independent violation of correlation inequalities for noncontextual theories,” Phys. Rev. Lett. 103, 050401 (2009).
    [Crossref]
  14. S. Yu and C. Oh, “State-independent proof of Kochen-Specker theorem with 13 rays,” Phys. Rev. Lett. 108, 030402 (2012).
    [Crossref]
  15. A. Cabello, E. Amselem, K. Blanchfield, M. Bourennane, and I. Bengtsson, “Proposed experiments of qutrit state-independent contextuality and two-qutrit contextuality-based nonlocality,” Phys. Rev. A 85, 032108 (2012).
    [Crossref]
  16. C. Zu, Y.-X. Wang, D.-L. Deng, X.-Y. Chang, K. Liu, P.-Y. Hou, H.-X. Yang, and L.-M. Duan, “State-independent experimental test of quantum contextuality in an indivisible system,” Phys. Rev. Lett. 109, 150401 (2012).
    [Crossref]
  17. X. Zhang, M. Um, J. Zhang, S. An, Y. Wang, D.-L. Deng, C. Shen, L.-M. Duan, and K. Kim, “State-independent experimental test of quantum contextuality with a single trapped ion,” Phys. Rev. Lett. 110, 070401 (2013).
    [Crossref]
  18. P. Busch, “Quantum states and generalized observables: a simple proof of Gleason’s theorem,” Phys. Rev. Lett. 91, 120403 (2003).
    [Crossref]
  19. A. Cabello, “Kochen-Specker theorem for a single qubit using positive operator-valued measures,” Phys. Rev. Lett. 90, 190401 (2003).
    [Crossref]
  20. P. Aravind, “Generalized Kochen-Specker theorem,” Phys. Rev. A 68, 052104 (2003).
    [Crossref]
  21. A. A. Méthot, “Minimal Bell-Kochen–Specker proofs with POVMs on qubits,” Int. J. Quantum Inf. 5, 353–357 (2007).
    [Crossref]
  22. R. W. Spekkens, “The status of determinism in proofs of the impossibility of a noncontextual model of quantum theory,” Found. Phys. 44, 1125–1155 (2014).
    [Crossref]
  23. Y.-C. Liang, R. W. Spekkens, and H. M. Wiseman, “Specker’s parable of the overprotective seer: a road to contextuality, nonlocality and complementarity,” Phys. Rep. 506, 1–39 (2011).
    [Crossref]
  24. R. Kunjwal and S. Ghosh, “Minimal state-dependent proof of measurement contextuality for a qubit,” Phys. Rev. A 89, 042118 (2014).
    [Crossref]
  25. M. D. Mazurek, M. F. Pusey, R. Kunjwal, K. J. Resch, and R. W. Spekkens, “An experimental test of noncontextuality without unphysical idealizations,” Nat. Commun. 7, ncomms11780 (2016).
    [Crossref]
  26. J. Thorn, M. Neel, V. Donato, G. Bergreen, R. Davies, and M. Beck, “Observing the quantum behavior of light in an undergraduate laboratory,” Am. J. Phys. 72, 1210–1219 (2004).
    [Crossref]
  27. J. Fiurášek, “Maximum-likelihood estimation of quantum measurement,” Phys. Rev. A 64, 024102 (2001).
    [Crossref]
  28. G. M. D’Ariano, M. G. Paris, and M. F. Sacchi, “Quantum tomography,” Adv. Imaging Electron Phys. 128, 206–309 (2003).
  29. B. A. Chase and J. Geremia, “Single-shot parameter estimation via continuous quantum measurement,” Phys. Rev. A 79, 022314 (2009).
    [Crossref]
  30. T. Konrad and H. Uys, “Maintaining quantum coherence in the presence of noise through state monitoring,” Phys. Rev. A 85, 012102 (2012).
    [Crossref]
  31. H. M. Wiseman, “Quantum control: squinting at quantum systems,” Nature 470, 178–179 (2011).
    [Crossref]

2016 (1)

M. D. Mazurek, M. F. Pusey, R. Kunjwal, K. J. Resch, and R. W. Spekkens, “An experimental test of noncontextuality without unphysical idealizations,” Nat. Commun. 7, ncomms11780 (2016).
[Crossref]

2014 (2)

R. Kunjwal and S. Ghosh, “Minimal state-dependent proof of measurement contextuality for a qubit,” Phys. Rev. A 89, 042118 (2014).
[Crossref]

R. W. Spekkens, “The status of determinism in proofs of the impossibility of a noncontextual model of quantum theory,” Found. Phys. 44, 1125–1155 (2014).
[Crossref]

2013 (1)

X. Zhang, M. Um, J. Zhang, S. An, Y. Wang, D.-L. Deng, C. Shen, L.-M. Duan, and K. Kim, “State-independent experimental test of quantum contextuality with a single trapped ion,” Phys. Rev. Lett. 110, 070401 (2013).
[Crossref]

2012 (4)

S. Yu and C. Oh, “State-independent proof of Kochen-Specker theorem with 13 rays,” Phys. Rev. Lett. 108, 030402 (2012).
[Crossref]

A. Cabello, E. Amselem, K. Blanchfield, M. Bourennane, and I. Bengtsson, “Proposed experiments of qutrit state-independent contextuality and two-qutrit contextuality-based nonlocality,” Phys. Rev. A 85, 032108 (2012).
[Crossref]

C. Zu, Y.-X. Wang, D.-L. Deng, X.-Y. Chang, K. Liu, P.-Y. Hou, H.-X. Yang, and L.-M. Duan, “State-independent experimental test of quantum contextuality in an indivisible system,” Phys. Rev. Lett. 109, 150401 (2012).
[Crossref]

T. Konrad and H. Uys, “Maintaining quantum coherence in the presence of noise through state monitoring,” Phys. Rev. A 85, 012102 (2012).
[Crossref]

2011 (3)

H. M. Wiseman, “Quantum control: squinting at quantum systems,” Nature 470, 178–179 (2011).
[Crossref]

Y.-C. Liang, R. W. Spekkens, and H. M. Wiseman, “Specker’s parable of the overprotective seer: a road to contextuality, nonlocality and complementarity,” Phys. Rep. 506, 1–39 (2011).
[Crossref]

R. Lapkiewicz, P. Li, C. Schaeff, N. K. Langford, S. Ramelow, M. Wieśniak, and A. Zeilinger, “Experimental non-classicality of an indivisible quantum system,” Nature 474, 490–493 (2011).
[Crossref]

2010 (1)

O. Moussa, C. A. Ryan, D. G. Cory, and R. Laflamme, “Testing contextuality on quantum ensembles with one clean qubit,” Phys. Rev. Lett. 104, 160501 (2010).
[Crossref]

2009 (5)

G. Kirchmair, F. Zähringer, R. Gerritsma, M. Kleinmann, O. Gühne, A. Cabello, R. Blatt, and C. F. Roos, “State-independent experimental test of quantum contextuality,” Nature 460, 494–497 (2009).
[Crossref]

E. Amselem, M. Rådmark, M. Bourennane, and A. Cabello, “State-independent quantum contextuality with single photons,” Phys. Rev. Lett. 103, 160405 (2009).
[Crossref]

H. Bartosik, J. Klepp, C. Schmitzer, S. Sponar, A. Cabello, H. Rauch, and Y. Hasegawa, “Experimental test of quantum contextuality in neutron interferometry,” Phys. Rev. Lett. 103, 040403 (2009).
[Crossref]

P. Badziag, I. Bengtsson, A. Cabello, and I. Pitowsky, “Universality of state-independent violation of correlation inequalities for noncontextual theories,” Phys. Rev. Lett. 103, 050401 (2009).
[Crossref]

B. A. Chase and J. Geremia, “Single-shot parameter estimation via continuous quantum measurement,” Phys. Rev. A 79, 022314 (2009).
[Crossref]

2008 (1)

A. A. Klyachko, M. A. Can, S. Binicioğlu, and A. S. Shumovsky, “Simple test for hidden variables in spin-1 systems,” Phys. Rev. Lett. 101, 020403 (2008).
[Crossref]

2007 (1)

A. A. Méthot, “Minimal Bell-Kochen–Specker proofs with POVMs on qubits,” Int. J. Quantum Inf. 5, 353–357 (2007).
[Crossref]

2004 (1)

J. Thorn, M. Neel, V. Donato, G. Bergreen, R. Davies, and M. Beck, “Observing the quantum behavior of light in an undergraduate laboratory,” Am. J. Phys. 72, 1210–1219 (2004).
[Crossref]

2003 (5)

G. M. D’Ariano, M. G. Paris, and M. F. Sacchi, “Quantum tomography,” Adv. Imaging Electron Phys. 128, 206–309 (2003).

Y.-F. Huang, C.-F. Li, Y.-S. Zhang, J.-W. Pan, and G.-C. Guo, “Experimental test of the Kochen-Specker theorem with single photons,” Phys. Rev. Lett. 90, 250401 (2003).
[Crossref]

P. Busch, “Quantum states and generalized observables: a simple proof of Gleason’s theorem,” Phys. Rev. Lett. 91, 120403 (2003).
[Crossref]

A. Cabello, “Kochen-Specker theorem for a single qubit using positive operator-valued measures,” Phys. Rev. Lett. 90, 190401 (2003).
[Crossref]

P. Aravind, “Generalized Kochen-Specker theorem,” Phys. Rev. A 68, 052104 (2003).
[Crossref]

2001 (1)

J. Fiurášek, “Maximum-likelihood estimation of quantum measurement,” Phys. Rev. A 64, 024102 (2001).
[Crossref]

1998 (1)

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of Bell’s inequality under strict Einstein locality conditions,” Phys. Rev. Lett. 81, 5039–5043 (1998).
[Crossref]

1996 (1)

J. Bub, “Schütte’s tautology and the Kochen-Specker theorem,” Found. Phys. 26, 787–806 (1996).
[Crossref]

1991 (1)

A. Peres, “Two simple proofs of the Kochen-Specker theorem,” J. Phys. A 24, L175 (1991).
[Crossref]

1967 (1)

S. Kochen and E. Specker, “The problem of hidden variables in quantum mechanics,” J. Math. Mech. 17, 59–87 (1967).
[Crossref]

1964 (1)

J. S. Bell, “On the Einstein Podolsky Rosen paradox,” Physics 1, 195–200 (1964).

Amselem, E.

A. Cabello, E. Amselem, K. Blanchfield, M. Bourennane, and I. Bengtsson, “Proposed experiments of qutrit state-independent contextuality and two-qutrit contextuality-based nonlocality,” Phys. Rev. A 85, 032108 (2012).
[Crossref]

E. Amselem, M. Rådmark, M. Bourennane, and A. Cabello, “State-independent quantum contextuality with single photons,” Phys. Rev. Lett. 103, 160405 (2009).
[Crossref]

An, S.

X. Zhang, M. Um, J. Zhang, S. An, Y. Wang, D.-L. Deng, C. Shen, L.-M. Duan, and K. Kim, “State-independent experimental test of quantum contextuality with a single trapped ion,” Phys. Rev. Lett. 110, 070401 (2013).
[Crossref]

Aravind, P.

P. Aravind, “Generalized Kochen-Specker theorem,” Phys. Rev. A 68, 052104 (2003).
[Crossref]

Badziag, P.

P. Badziag, I. Bengtsson, A. Cabello, and I. Pitowsky, “Universality of state-independent violation of correlation inequalities for noncontextual theories,” Phys. Rev. Lett. 103, 050401 (2009).
[Crossref]

Bartosik, H.

H. Bartosik, J. Klepp, C. Schmitzer, S. Sponar, A. Cabello, H. Rauch, and Y. Hasegawa, “Experimental test of quantum contextuality in neutron interferometry,” Phys. Rev. Lett. 103, 040403 (2009).
[Crossref]

Beck, M.

J. Thorn, M. Neel, V. Donato, G. Bergreen, R. Davies, and M. Beck, “Observing the quantum behavior of light in an undergraduate laboratory,” Am. J. Phys. 72, 1210–1219 (2004).
[Crossref]

Bell, J. S.

J. S. Bell, “On the Einstein Podolsky Rosen paradox,” Physics 1, 195–200 (1964).

Bengtsson, I.

A. Cabello, E. Amselem, K. Blanchfield, M. Bourennane, and I. Bengtsson, “Proposed experiments of qutrit state-independent contextuality and two-qutrit contextuality-based nonlocality,” Phys. Rev. A 85, 032108 (2012).
[Crossref]

P. Badziag, I. Bengtsson, A. Cabello, and I. Pitowsky, “Universality of state-independent violation of correlation inequalities for noncontextual theories,” Phys. Rev. Lett. 103, 050401 (2009).
[Crossref]

Bergreen, G.

J. Thorn, M. Neel, V. Donato, G. Bergreen, R. Davies, and M. Beck, “Observing the quantum behavior of light in an undergraduate laboratory,” Am. J. Phys. 72, 1210–1219 (2004).
[Crossref]

Binicioglu, S.

A. A. Klyachko, M. A. Can, S. Binicioğlu, and A. S. Shumovsky, “Simple test for hidden variables in spin-1 systems,” Phys. Rev. Lett. 101, 020403 (2008).
[Crossref]

Blanchfield, K.

A. Cabello, E. Amselem, K. Blanchfield, M. Bourennane, and I. Bengtsson, “Proposed experiments of qutrit state-independent contextuality and two-qutrit contextuality-based nonlocality,” Phys. Rev. A 85, 032108 (2012).
[Crossref]

Blatt, R.

G. Kirchmair, F. Zähringer, R. Gerritsma, M. Kleinmann, O. Gühne, A. Cabello, R. Blatt, and C. F. Roos, “State-independent experimental test of quantum contextuality,” Nature 460, 494–497 (2009).
[Crossref]

Bourennane, M.

A. Cabello, E. Amselem, K. Blanchfield, M. Bourennane, and I. Bengtsson, “Proposed experiments of qutrit state-independent contextuality and two-qutrit contextuality-based nonlocality,” Phys. Rev. A 85, 032108 (2012).
[Crossref]

E. Amselem, M. Rådmark, M. Bourennane, and A. Cabello, “State-independent quantum contextuality with single photons,” Phys. Rev. Lett. 103, 160405 (2009).
[Crossref]

Bub, J.

J. Bub, “Schütte’s tautology and the Kochen-Specker theorem,” Found. Phys. 26, 787–806 (1996).
[Crossref]

Busch, P.

P. Busch, “Quantum states and generalized observables: a simple proof of Gleason’s theorem,” Phys. Rev. Lett. 91, 120403 (2003).
[Crossref]

Cabello, A.

A. Cabello, E. Amselem, K. Blanchfield, M. Bourennane, and I. Bengtsson, “Proposed experiments of qutrit state-independent contextuality and two-qutrit contextuality-based nonlocality,” Phys. Rev. A 85, 032108 (2012).
[Crossref]

P. Badziag, I. Bengtsson, A. Cabello, and I. Pitowsky, “Universality of state-independent violation of correlation inequalities for noncontextual theories,” Phys. Rev. Lett. 103, 050401 (2009).
[Crossref]

G. Kirchmair, F. Zähringer, R. Gerritsma, M. Kleinmann, O. Gühne, A. Cabello, R. Blatt, and C. F. Roos, “State-independent experimental test of quantum contextuality,” Nature 460, 494–497 (2009).
[Crossref]

E. Amselem, M. Rådmark, M. Bourennane, and A. Cabello, “State-independent quantum contextuality with single photons,” Phys. Rev. Lett. 103, 160405 (2009).
[Crossref]

H. Bartosik, J. Klepp, C. Schmitzer, S. Sponar, A. Cabello, H. Rauch, and Y. Hasegawa, “Experimental test of quantum contextuality in neutron interferometry,” Phys. Rev. Lett. 103, 040403 (2009).
[Crossref]

A. Cabello, “Kochen-Specker theorem for a single qubit using positive operator-valued measures,” Phys. Rev. Lett. 90, 190401 (2003).
[Crossref]

Can, M. A.

A. A. Klyachko, M. A. Can, S. Binicioğlu, and A. S. Shumovsky, “Simple test for hidden variables in spin-1 systems,” Phys. Rev. Lett. 101, 020403 (2008).
[Crossref]

Chang, X.-Y.

C. Zu, Y.-X. Wang, D.-L. Deng, X.-Y. Chang, K. Liu, P.-Y. Hou, H.-X. Yang, and L.-M. Duan, “State-independent experimental test of quantum contextuality in an indivisible system,” Phys. Rev. Lett. 109, 150401 (2012).
[Crossref]

Chase, B. A.

B. A. Chase and J. Geremia, “Single-shot parameter estimation via continuous quantum measurement,” Phys. Rev. A 79, 022314 (2009).
[Crossref]

Cory, D. G.

O. Moussa, C. A. Ryan, D. G. Cory, and R. Laflamme, “Testing contextuality on quantum ensembles with one clean qubit,” Phys. Rev. Lett. 104, 160501 (2010).
[Crossref]

D’Ariano, G. M.

G. M. D’Ariano, M. G. Paris, and M. F. Sacchi, “Quantum tomography,” Adv. Imaging Electron Phys. 128, 206–309 (2003).

Davies, R.

J. Thorn, M. Neel, V. Donato, G. Bergreen, R. Davies, and M. Beck, “Observing the quantum behavior of light in an undergraduate laboratory,” Am. J. Phys. 72, 1210–1219 (2004).
[Crossref]

Deng, D.-L.

X. Zhang, M. Um, J. Zhang, S. An, Y. Wang, D.-L. Deng, C. Shen, L.-M. Duan, and K. Kim, “State-independent experimental test of quantum contextuality with a single trapped ion,” Phys. Rev. Lett. 110, 070401 (2013).
[Crossref]

C. Zu, Y.-X. Wang, D.-L. Deng, X.-Y. Chang, K. Liu, P.-Y. Hou, H.-X. Yang, and L.-M. Duan, “State-independent experimental test of quantum contextuality in an indivisible system,” Phys. Rev. Lett. 109, 150401 (2012).
[Crossref]

Donato, V.

J. Thorn, M. Neel, V. Donato, G. Bergreen, R. Davies, and M. Beck, “Observing the quantum behavior of light in an undergraduate laboratory,” Am. J. Phys. 72, 1210–1219 (2004).
[Crossref]

Duan, L.-M.

X. Zhang, M. Um, J. Zhang, S. An, Y. Wang, D.-L. Deng, C. Shen, L.-M. Duan, and K. Kim, “State-independent experimental test of quantum contextuality with a single trapped ion,” Phys. Rev. Lett. 110, 070401 (2013).
[Crossref]

C. Zu, Y.-X. Wang, D.-L. Deng, X.-Y. Chang, K. Liu, P.-Y. Hou, H.-X. Yang, and L.-M. Duan, “State-independent experimental test of quantum contextuality in an indivisible system,” Phys. Rev. Lett. 109, 150401 (2012).
[Crossref]

Fiurášek, J.

J. Fiurášek, “Maximum-likelihood estimation of quantum measurement,” Phys. Rev. A 64, 024102 (2001).
[Crossref]

Geremia, J.

B. A. Chase and J. Geremia, “Single-shot parameter estimation via continuous quantum measurement,” Phys. Rev. A 79, 022314 (2009).
[Crossref]

Gerritsma, R.

G. Kirchmair, F. Zähringer, R. Gerritsma, M. Kleinmann, O. Gühne, A. Cabello, R. Blatt, and C. F. Roos, “State-independent experimental test of quantum contextuality,” Nature 460, 494–497 (2009).
[Crossref]

Ghosh, S.

R. Kunjwal and S. Ghosh, “Minimal state-dependent proof of measurement contextuality for a qubit,” Phys. Rev. A 89, 042118 (2014).
[Crossref]

Gühne, O.

G. Kirchmair, F. Zähringer, R. Gerritsma, M. Kleinmann, O. Gühne, A. Cabello, R. Blatt, and C. F. Roos, “State-independent experimental test of quantum contextuality,” Nature 460, 494–497 (2009).
[Crossref]

Guo, G.-C.

Y.-F. Huang, C.-F. Li, Y.-S. Zhang, J.-W. Pan, and G.-C. Guo, “Experimental test of the Kochen-Specker theorem with single photons,” Phys. Rev. Lett. 90, 250401 (2003).
[Crossref]

Hasegawa, Y.

H. Bartosik, J. Klepp, C. Schmitzer, S. Sponar, A. Cabello, H. Rauch, and Y. Hasegawa, “Experimental test of quantum contextuality in neutron interferometry,” Phys. Rev. Lett. 103, 040403 (2009).
[Crossref]

Hou, P.-Y.

C. Zu, Y.-X. Wang, D.-L. Deng, X.-Y. Chang, K. Liu, P.-Y. Hou, H.-X. Yang, and L.-M. Duan, “State-independent experimental test of quantum contextuality in an indivisible system,” Phys. Rev. Lett. 109, 150401 (2012).
[Crossref]

Huang, Y.-F.

Y.-F. Huang, C.-F. Li, Y.-S. Zhang, J.-W. Pan, and G.-C. Guo, “Experimental test of the Kochen-Specker theorem with single photons,” Phys. Rev. Lett. 90, 250401 (2003).
[Crossref]

Jennewein, T.

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of Bell’s inequality under strict Einstein locality conditions,” Phys. Rev. Lett. 81, 5039–5043 (1998).
[Crossref]

Kim, K.

X. Zhang, M. Um, J. Zhang, S. An, Y. Wang, D.-L. Deng, C. Shen, L.-M. Duan, and K. Kim, “State-independent experimental test of quantum contextuality with a single trapped ion,” Phys. Rev. Lett. 110, 070401 (2013).
[Crossref]

Kirchmair, G.

G. Kirchmair, F. Zähringer, R. Gerritsma, M. Kleinmann, O. Gühne, A. Cabello, R. Blatt, and C. F. Roos, “State-independent experimental test of quantum contextuality,” Nature 460, 494–497 (2009).
[Crossref]

Kleinmann, M.

G. Kirchmair, F. Zähringer, R. Gerritsma, M. Kleinmann, O. Gühne, A. Cabello, R. Blatt, and C. F. Roos, “State-independent experimental test of quantum contextuality,” Nature 460, 494–497 (2009).
[Crossref]

Klepp, J.

H. Bartosik, J. Klepp, C. Schmitzer, S. Sponar, A. Cabello, H. Rauch, and Y. Hasegawa, “Experimental test of quantum contextuality in neutron interferometry,” Phys. Rev. Lett. 103, 040403 (2009).
[Crossref]

Klyachko, A. A.

A. A. Klyachko, M. A. Can, S. Binicioğlu, and A. S. Shumovsky, “Simple test for hidden variables in spin-1 systems,” Phys. Rev. Lett. 101, 020403 (2008).
[Crossref]

Kochen, S.

S. Kochen and E. Specker, “The problem of hidden variables in quantum mechanics,” J. Math. Mech. 17, 59–87 (1967).
[Crossref]

Konrad, T.

T. Konrad and H. Uys, “Maintaining quantum coherence in the presence of noise through state monitoring,” Phys. Rev. A 85, 012102 (2012).
[Crossref]

Kunjwal, R.

M. D. Mazurek, M. F. Pusey, R. Kunjwal, K. J. Resch, and R. W. Spekkens, “An experimental test of noncontextuality without unphysical idealizations,” Nat. Commun. 7, ncomms11780 (2016).
[Crossref]

R. Kunjwal and S. Ghosh, “Minimal state-dependent proof of measurement contextuality for a qubit,” Phys. Rev. A 89, 042118 (2014).
[Crossref]

Laflamme, R.

O. Moussa, C. A. Ryan, D. G. Cory, and R. Laflamme, “Testing contextuality on quantum ensembles with one clean qubit,” Phys. Rev. Lett. 104, 160501 (2010).
[Crossref]

Langford, N. K.

R. Lapkiewicz, P. Li, C. Schaeff, N. K. Langford, S. Ramelow, M. Wieśniak, and A. Zeilinger, “Experimental non-classicality of an indivisible quantum system,” Nature 474, 490–493 (2011).
[Crossref]

Lapkiewicz, R.

R. Lapkiewicz, P. Li, C. Schaeff, N. K. Langford, S. Ramelow, M. Wieśniak, and A. Zeilinger, “Experimental non-classicality of an indivisible quantum system,” Nature 474, 490–493 (2011).
[Crossref]

Li, C.-F.

Y.-F. Huang, C.-F. Li, Y.-S. Zhang, J.-W. Pan, and G.-C. Guo, “Experimental test of the Kochen-Specker theorem with single photons,” Phys. Rev. Lett. 90, 250401 (2003).
[Crossref]

Li, P.

R. Lapkiewicz, P. Li, C. Schaeff, N. K. Langford, S. Ramelow, M. Wieśniak, and A. Zeilinger, “Experimental non-classicality of an indivisible quantum system,” Nature 474, 490–493 (2011).
[Crossref]

Liang, Y.-C.

Y.-C. Liang, R. W. Spekkens, and H. M. Wiseman, “Specker’s parable of the overprotective seer: a road to contextuality, nonlocality and complementarity,” Phys. Rep. 506, 1–39 (2011).
[Crossref]

Liu, K.

C. Zu, Y.-X. Wang, D.-L. Deng, X.-Y. Chang, K. Liu, P.-Y. Hou, H.-X. Yang, and L.-M. Duan, “State-independent experimental test of quantum contextuality in an indivisible system,” Phys. Rev. Lett. 109, 150401 (2012).
[Crossref]

Mazurek, M. D.

M. D. Mazurek, M. F. Pusey, R. Kunjwal, K. J. Resch, and R. W. Spekkens, “An experimental test of noncontextuality without unphysical idealizations,” Nat. Commun. 7, ncomms11780 (2016).
[Crossref]

Méthot, A. A.

A. A. Méthot, “Minimal Bell-Kochen–Specker proofs with POVMs on qubits,” Int. J. Quantum Inf. 5, 353–357 (2007).
[Crossref]

Moussa, O.

O. Moussa, C. A. Ryan, D. G. Cory, and R. Laflamme, “Testing contextuality on quantum ensembles with one clean qubit,” Phys. Rev. Lett. 104, 160501 (2010).
[Crossref]

Neel, M.

J. Thorn, M. Neel, V. Donato, G. Bergreen, R. Davies, and M. Beck, “Observing the quantum behavior of light in an undergraduate laboratory,” Am. J. Phys. 72, 1210–1219 (2004).
[Crossref]

Oh, C.

S. Yu and C. Oh, “State-independent proof of Kochen-Specker theorem with 13 rays,” Phys. Rev. Lett. 108, 030402 (2012).
[Crossref]

Pan, J.-W.

Y.-F. Huang, C.-F. Li, Y.-S. Zhang, J.-W. Pan, and G.-C. Guo, “Experimental test of the Kochen-Specker theorem with single photons,” Phys. Rev. Lett. 90, 250401 (2003).
[Crossref]

Paris, M. G.

G. M. D’Ariano, M. G. Paris, and M. F. Sacchi, “Quantum tomography,” Adv. Imaging Electron Phys. 128, 206–309 (2003).

Peres, A.

A. Peres, “Two simple proofs of the Kochen-Specker theorem,” J. Phys. A 24, L175 (1991).
[Crossref]

Pitowsky, I.

P. Badziag, I. Bengtsson, A. Cabello, and I. Pitowsky, “Universality of state-independent violation of correlation inequalities for noncontextual theories,” Phys. Rev. Lett. 103, 050401 (2009).
[Crossref]

Pusey, M. F.

M. D. Mazurek, M. F. Pusey, R. Kunjwal, K. J. Resch, and R. W. Spekkens, “An experimental test of noncontextuality without unphysical idealizations,” Nat. Commun. 7, ncomms11780 (2016).
[Crossref]

Rådmark, M.

E. Amselem, M. Rådmark, M. Bourennane, and A. Cabello, “State-independent quantum contextuality with single photons,” Phys. Rev. Lett. 103, 160405 (2009).
[Crossref]

Ramelow, S.

R. Lapkiewicz, P. Li, C. Schaeff, N. K. Langford, S. Ramelow, M. Wieśniak, and A. Zeilinger, “Experimental non-classicality of an indivisible quantum system,” Nature 474, 490–493 (2011).
[Crossref]

Rauch, H.

H. Bartosik, J. Klepp, C. Schmitzer, S. Sponar, A. Cabello, H. Rauch, and Y. Hasegawa, “Experimental test of quantum contextuality in neutron interferometry,” Phys. Rev. Lett. 103, 040403 (2009).
[Crossref]

Resch, K. J.

M. D. Mazurek, M. F. Pusey, R. Kunjwal, K. J. Resch, and R. W. Spekkens, “An experimental test of noncontextuality without unphysical idealizations,” Nat. Commun. 7, ncomms11780 (2016).
[Crossref]

Roos, C. F.

G. Kirchmair, F. Zähringer, R. Gerritsma, M. Kleinmann, O. Gühne, A. Cabello, R. Blatt, and C. F. Roos, “State-independent experimental test of quantum contextuality,” Nature 460, 494–497 (2009).
[Crossref]

Ryan, C. A.

O. Moussa, C. A. Ryan, D. G. Cory, and R. Laflamme, “Testing contextuality on quantum ensembles with one clean qubit,” Phys. Rev. Lett. 104, 160501 (2010).
[Crossref]

Sacchi, M. F.

G. M. D’Ariano, M. G. Paris, and M. F. Sacchi, “Quantum tomography,” Adv. Imaging Electron Phys. 128, 206–309 (2003).

Schaeff, C.

R. Lapkiewicz, P. Li, C. Schaeff, N. K. Langford, S. Ramelow, M. Wieśniak, and A. Zeilinger, “Experimental non-classicality of an indivisible quantum system,” Nature 474, 490–493 (2011).
[Crossref]

Schmitzer, C.

H. Bartosik, J. Klepp, C. Schmitzer, S. Sponar, A. Cabello, H. Rauch, and Y. Hasegawa, “Experimental test of quantum contextuality in neutron interferometry,” Phys. Rev. Lett. 103, 040403 (2009).
[Crossref]

Shen, C.

X. Zhang, M. Um, J. Zhang, S. An, Y. Wang, D.-L. Deng, C. Shen, L.-M. Duan, and K. Kim, “State-independent experimental test of quantum contextuality with a single trapped ion,” Phys. Rev. Lett. 110, 070401 (2013).
[Crossref]

Shumovsky, A. S.

A. A. Klyachko, M. A. Can, S. Binicioğlu, and A. S. Shumovsky, “Simple test for hidden variables in spin-1 systems,” Phys. Rev. Lett. 101, 020403 (2008).
[Crossref]

Simon, C.

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of Bell’s inequality under strict Einstein locality conditions,” Phys. Rev. Lett. 81, 5039–5043 (1998).
[Crossref]

Specker, E.

S. Kochen and E. Specker, “The problem of hidden variables in quantum mechanics,” J. Math. Mech. 17, 59–87 (1967).
[Crossref]

Spekkens, R. W.

M. D. Mazurek, M. F. Pusey, R. Kunjwal, K. J. Resch, and R. W. Spekkens, “An experimental test of noncontextuality without unphysical idealizations,” Nat. Commun. 7, ncomms11780 (2016).
[Crossref]

R. W. Spekkens, “The status of determinism in proofs of the impossibility of a noncontextual model of quantum theory,” Found. Phys. 44, 1125–1155 (2014).
[Crossref]

Y.-C. Liang, R. W. Spekkens, and H. M. Wiseman, “Specker’s parable of the overprotective seer: a road to contextuality, nonlocality and complementarity,” Phys. Rep. 506, 1–39 (2011).
[Crossref]

Sponar, S.

H. Bartosik, J. Klepp, C. Schmitzer, S. Sponar, A. Cabello, H. Rauch, and Y. Hasegawa, “Experimental test of quantum contextuality in neutron interferometry,” Phys. Rev. Lett. 103, 040403 (2009).
[Crossref]

Thorn, J.

J. Thorn, M. Neel, V. Donato, G. Bergreen, R. Davies, and M. Beck, “Observing the quantum behavior of light in an undergraduate laboratory,” Am. J. Phys. 72, 1210–1219 (2004).
[Crossref]

Um, M.

X. Zhang, M. Um, J. Zhang, S. An, Y. Wang, D.-L. Deng, C. Shen, L.-M. Duan, and K. Kim, “State-independent experimental test of quantum contextuality with a single trapped ion,” Phys. Rev. Lett. 110, 070401 (2013).
[Crossref]

Uys, H.

T. Konrad and H. Uys, “Maintaining quantum coherence in the presence of noise through state monitoring,” Phys. Rev. A 85, 012102 (2012).
[Crossref]

Wang, Y.

X. Zhang, M. Um, J. Zhang, S. An, Y. Wang, D.-L. Deng, C. Shen, L.-M. Duan, and K. Kim, “State-independent experimental test of quantum contextuality with a single trapped ion,” Phys. Rev. Lett. 110, 070401 (2013).
[Crossref]

Wang, Y.-X.

C. Zu, Y.-X. Wang, D.-L. Deng, X.-Y. Chang, K. Liu, P.-Y. Hou, H.-X. Yang, and L.-M. Duan, “State-independent experimental test of quantum contextuality in an indivisible system,” Phys. Rev. Lett. 109, 150401 (2012).
[Crossref]

Weihs, G.

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of Bell’s inequality under strict Einstein locality conditions,” Phys. Rev. Lett. 81, 5039–5043 (1998).
[Crossref]

Weinfurter, H.

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of Bell’s inequality under strict Einstein locality conditions,” Phys. Rev. Lett. 81, 5039–5043 (1998).
[Crossref]

Wiesniak, M.

R. Lapkiewicz, P. Li, C. Schaeff, N. K. Langford, S. Ramelow, M. Wieśniak, and A. Zeilinger, “Experimental non-classicality of an indivisible quantum system,” Nature 474, 490–493 (2011).
[Crossref]

Wiseman, H. M.

Y.-C. Liang, R. W. Spekkens, and H. M. Wiseman, “Specker’s parable of the overprotective seer: a road to contextuality, nonlocality and complementarity,” Phys. Rep. 506, 1–39 (2011).
[Crossref]

H. M. Wiseman, “Quantum control: squinting at quantum systems,” Nature 470, 178–179 (2011).
[Crossref]

Yang, H.-X.

C. Zu, Y.-X. Wang, D.-L. Deng, X.-Y. Chang, K. Liu, P.-Y. Hou, H.-X. Yang, and L.-M. Duan, “State-independent experimental test of quantum contextuality in an indivisible system,” Phys. Rev. Lett. 109, 150401 (2012).
[Crossref]

Yu, S.

S. Yu and C. Oh, “State-independent proof of Kochen-Specker theorem with 13 rays,” Phys. Rev. Lett. 108, 030402 (2012).
[Crossref]

Zähringer, F.

G. Kirchmair, F. Zähringer, R. Gerritsma, M. Kleinmann, O. Gühne, A. Cabello, R. Blatt, and C. F. Roos, “State-independent experimental test of quantum contextuality,” Nature 460, 494–497 (2009).
[Crossref]

Zeilinger, A.

R. Lapkiewicz, P. Li, C. Schaeff, N. K. Langford, S. Ramelow, M. Wieśniak, and A. Zeilinger, “Experimental non-classicality of an indivisible quantum system,” Nature 474, 490–493 (2011).
[Crossref]

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of Bell’s inequality under strict Einstein locality conditions,” Phys. Rev. Lett. 81, 5039–5043 (1998).
[Crossref]

Zhang, J.

X. Zhang, M. Um, J. Zhang, S. An, Y. Wang, D.-L. Deng, C. Shen, L.-M. Duan, and K. Kim, “State-independent experimental test of quantum contextuality with a single trapped ion,” Phys. Rev. Lett. 110, 070401 (2013).
[Crossref]

Zhang, X.

X. Zhang, M. Um, J. Zhang, S. An, Y. Wang, D.-L. Deng, C. Shen, L.-M. Duan, and K. Kim, “State-independent experimental test of quantum contextuality with a single trapped ion,” Phys. Rev. Lett. 110, 070401 (2013).
[Crossref]

Zhang, Y.-S.

Y.-F. Huang, C.-F. Li, Y.-S. Zhang, J.-W. Pan, and G.-C. Guo, “Experimental test of the Kochen-Specker theorem with single photons,” Phys. Rev. Lett. 90, 250401 (2003).
[Crossref]

Zu, C.

C. Zu, Y.-X. Wang, D.-L. Deng, X.-Y. Chang, K. Liu, P.-Y. Hou, H.-X. Yang, and L.-M. Duan, “State-independent experimental test of quantum contextuality in an indivisible system,” Phys. Rev. Lett. 109, 150401 (2012).
[Crossref]

Adv. Imaging Electron Phys. (1)

G. M. D’Ariano, M. G. Paris, and M. F. Sacchi, “Quantum tomography,” Adv. Imaging Electron Phys. 128, 206–309 (2003).

Am. J. Phys. (1)

J. Thorn, M. Neel, V. Donato, G. Bergreen, R. Davies, and M. Beck, “Observing the quantum behavior of light in an undergraduate laboratory,” Am. J. Phys. 72, 1210–1219 (2004).
[Crossref]

Found. Phys. (2)

R. W. Spekkens, “The status of determinism in proofs of the impossibility of a noncontextual model of quantum theory,” Found. Phys. 44, 1125–1155 (2014).
[Crossref]

J. Bub, “Schütte’s tautology and the Kochen-Specker theorem,” Found. Phys. 26, 787–806 (1996).
[Crossref]

Int. J. Quantum Inf. (1)

A. A. Méthot, “Minimal Bell-Kochen–Specker proofs with POVMs on qubits,” Int. J. Quantum Inf. 5, 353–357 (2007).
[Crossref]

J. Math. Mech. (1)

S. Kochen and E. Specker, “The problem of hidden variables in quantum mechanics,” J. Math. Mech. 17, 59–87 (1967).
[Crossref]

J. Phys. A (1)

A. Peres, “Two simple proofs of the Kochen-Specker theorem,” J. Phys. A 24, L175 (1991).
[Crossref]

Nat. Commun. (1)

M. D. Mazurek, M. F. Pusey, R. Kunjwal, K. J. Resch, and R. W. Spekkens, “An experimental test of noncontextuality without unphysical idealizations,” Nat. Commun. 7, ncomms11780 (2016).
[Crossref]

Nature (3)

H. M. Wiseman, “Quantum control: squinting at quantum systems,” Nature 470, 178–179 (2011).
[Crossref]

R. Lapkiewicz, P. Li, C. Schaeff, N. K. Langford, S. Ramelow, M. Wieśniak, and A. Zeilinger, “Experimental non-classicality of an indivisible quantum system,” Nature 474, 490–493 (2011).
[Crossref]

G. Kirchmair, F. Zähringer, R. Gerritsma, M. Kleinmann, O. Gühne, A. Cabello, R. Blatt, and C. F. Roos, “State-independent experimental test of quantum contextuality,” Nature 460, 494–497 (2009).
[Crossref]

Phys. Rep. (1)

Y.-C. Liang, R. W. Spekkens, and H. M. Wiseman, “Specker’s parable of the overprotective seer: a road to contextuality, nonlocality and complementarity,” Phys. Rep. 506, 1–39 (2011).
[Crossref]

Phys. Rev. A (6)

R. Kunjwal and S. Ghosh, “Minimal state-dependent proof of measurement contextuality for a qubit,” Phys. Rev. A 89, 042118 (2014).
[Crossref]

P. Aravind, “Generalized Kochen-Specker theorem,” Phys. Rev. A 68, 052104 (2003).
[Crossref]

J. Fiurášek, “Maximum-likelihood estimation of quantum measurement,” Phys. Rev. A 64, 024102 (2001).
[Crossref]

B. A. Chase and J. Geremia, “Single-shot parameter estimation via continuous quantum measurement,” Phys. Rev. A 79, 022314 (2009).
[Crossref]

T. Konrad and H. Uys, “Maintaining quantum coherence in the presence of noise through state monitoring,” Phys. Rev. A 85, 012102 (2012).
[Crossref]

A. Cabello, E. Amselem, K. Blanchfield, M. Bourennane, and I. Bengtsson, “Proposed experiments of qutrit state-independent contextuality and two-qutrit contextuality-based nonlocality,” Phys. Rev. A 85, 032108 (2012).
[Crossref]

Phys. Rev. Lett. (12)

C. Zu, Y.-X. Wang, D.-L. Deng, X.-Y. Chang, K. Liu, P.-Y. Hou, H.-X. Yang, and L.-M. Duan, “State-independent experimental test of quantum contextuality in an indivisible system,” Phys. Rev. Lett. 109, 150401 (2012).
[Crossref]

X. Zhang, M. Um, J. Zhang, S. An, Y. Wang, D.-L. Deng, C. Shen, L.-M. Duan, and K. Kim, “State-independent experimental test of quantum contextuality with a single trapped ion,” Phys. Rev. Lett. 110, 070401 (2013).
[Crossref]

P. Busch, “Quantum states and generalized observables: a simple proof of Gleason’s theorem,” Phys. Rev. Lett. 91, 120403 (2003).
[Crossref]

A. Cabello, “Kochen-Specker theorem for a single qubit using positive operator-valued measures,” Phys. Rev. Lett. 90, 190401 (2003).
[Crossref]

P. Badziag, I. Bengtsson, A. Cabello, and I. Pitowsky, “Universality of state-independent violation of correlation inequalities for noncontextual theories,” Phys. Rev. Lett. 103, 050401 (2009).
[Crossref]

S. Yu and C. Oh, “State-independent proof of Kochen-Specker theorem with 13 rays,” Phys. Rev. Lett. 108, 030402 (2012).
[Crossref]

E. Amselem, M. Rådmark, M. Bourennane, and A. Cabello, “State-independent quantum contextuality with single photons,” Phys. Rev. Lett. 103, 160405 (2009).
[Crossref]

H. Bartosik, J. Klepp, C. Schmitzer, S. Sponar, A. Cabello, H. Rauch, and Y. Hasegawa, “Experimental test of quantum contextuality in neutron interferometry,” Phys. Rev. Lett. 103, 040403 (2009).
[Crossref]

O. Moussa, C. A. Ryan, D. G. Cory, and R. Laflamme, “Testing contextuality on quantum ensembles with one clean qubit,” Phys. Rev. Lett. 104, 160501 (2010).
[Crossref]

A. A. Klyachko, M. A. Can, S. Binicioğlu, and A. S. Shumovsky, “Simple test for hidden variables in spin-1 systems,” Phys. Rev. Lett. 101, 020403 (2008).
[Crossref]

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, “Violation of Bell’s inequality under strict Einstein locality conditions,” Phys. Rev. Lett. 81, 5039–5043 (1998).
[Crossref]

Y.-F. Huang, C.-F. Li, Y.-S. Zhang, J.-W. Pan, and G.-C. Guo, “Experimental test of the Kochen-Specker theorem with single photons,” Phys. Rev. Lett. 90, 250401 (2003).
[Crossref]

Physics (1)

J. S. Bell, “On the Einstein Podolsky Rosen paradox,” Physics 1, 195–200 (1964).

Supplementary Material (1)

NameDescription
» Supplement 1       Experimental generalized contextuality with single-photon qubits: supplementary material

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Figures (3)

Fig. 1.
Fig. 1.

Experimental setup. Single photons are created via Type-I spontaneous parametric down-conversion (SPDC) in a 0.5 mm thick nonlinear-β-barium-borate (BBO) crystal, which is pumped by a CW diode laser with 80 mW of power. One photon in the pair is detected to herald the other photon, which is injected into the optical network. To realize the joint POVM Jij, the single-qubit rotations Uεϵ are realized by sandwich-type QWP–HWP–QWP sets with different angles placed in different optical modes. The first two projectors are realized by PPBSs with different transmission probabilities for vertical polarization. The last projector is realized by a PBS. Detecting heralded single photons means in practice registering coincidences between single photon detectors: D0 and each of D1–D4.

Fig. 2.
Fig. 2.

Distance D(E˜i(j),E˜i(k)) between the estimated POVM elements for different contexts {Mi,Mj} and {Mi,Mk}. Error bars indicate the statistical uncertainty, obtained from Monte Carlo simulations assuming Poissonian photon-counting statistics.

Fig. 3.
Fig. 3.

Distance D(Ei,E˜i(j)) between the aimed-for POVM element Ei for context {Mi,Mj} and the estimated POVM elements from the experiment E˜i(j). Error bars indicate the statistical uncertainty, obtained from Monte Carlo simulations assuming Poissonian photon-counting statistics.

Tables (1)

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Table 1. Experimental Resultsa

Equations (12)

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E±k121±η2σ·n^k=1η21+ηΠ±k.
n^1=(0,0,1),n^2=(32,0,12),n^3=(32,0,12),
G++ij=12{αij21+σ·12[η(n^i+n^j)aij]},G+ij=12{(1αij2)1+σ·12[η(n^in^j)+aij]},G+ij=12{(1αij2)1+σ·12[η(n^i+n^j)+aij]},Gij=12{αij21+σ·12[η(n^in^j)aij]},
R313(ij){(12),(23),(13)}Pr(XiXj|Jij)1η3,
R3Q=13(ij){(12),(23),(13)}Tr[(G+ij+G+ij)|ϕ0ϕ0|],
Uεϵ=|0ϕεϵ|+|1ϕεϵ|,εϵ{+,+,++},
Pεϵ0=|00|+(1χεϵ)|11|,Pεϵ1=χεϵ|11|.
D(A,B)=Tr[(AB)2]Tr(A2).
η˜εi(j)=2Tr[E˜εi(j)(E˜εi(j))]1.
Pr(G)Pr(G˜)12|gg˜|.
R3QR˜3Q132(ij)(12),(23),(13)(|g+ijg˜+ij|+|g+ijg˜+ij|).
R3Q0.7964±0.0012.

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