Specker's fundamental principle of quantum mechanics

S. Kochen and E. P. Specker, “The problem of hidden variables in quantum mechanics”, J. Math. Mech. 17

1967

Earlier work this paper cites.

J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to test local hidden-variable theories”, Phys. Rev. Lett. 23

1969

Earlier work this paper cites.

E. P. Specker, “Die Logik nicht gleichzeitig entscheidbarer Aussagen”, Dialectica 14

Original

1975

Earlier work this paper cites.

N. D. Mermin, “Extreme quantum entanglement in a superposition of macroscopically distinct states”, Phys. Rev. Lett. 65

1990

Cited alongside, same era.

S. Popescu and D. Rohrlich, “Quantum nonlocality as an axiom”, Found. Phys. 24

1994

Cited alongside, same era.

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

2008

Cited alongside, same era.

J. Henson, “Quantum contextuality from a simple principle”, e-print eprint arXiv:1210.5978v1 [quant-ph]

Original

Cited in the paper.

A. Cabello, “A simple explanation of the quantum violation of a fundamental inequality”, e-print eprint arXiv:1210.2988v1 [quant-ph]

Original

Cited in the paper.

T. Fritz, A. B. Sainz, R. Augusiak, J. Bohr Brask, R. Chaves, A. Leverrier, and A. Acín, “Local orthogonality: A multipartite principle for correlations”, e-print eprint arXiv:1210.3018 [quant-ph]

Original

Cited in the paper.

E. P. Specker, https://vimeo.com/52923835

Cited in the paper.

A. Cabello, S. Severini, and A. Winter, “ (Non-)

Original

Cited in the paper.

G. Boole, “On the theory of probabilities”, Phil. Trans. R. Soc. Lond. 152

Cited in the paper.

Notice that I say “a convex combination” not “any convex combination”, since my purpose here is to explain the maximum quantum correlations represented by G G , not the maximum quantum value of any correlations represented by G G . The following example illustrates the difference: the maximum quantum value for the I 3322 I_{3322} Bell inequality, represented by the graph G ⁡ ( I 3322 ) G(I_{3322}) , is smaller than the maximum quantum value that some correlations represented by the same graph G ⁡ ( I 3322 ) G(I_{3322}) can attain. My purpose here is to understand this second maximum, not the first one. A method to obtain explicit quantum correlations reaching this second maximum is described in Ref. [ 15 ]

Cited in the paper.

A. Cabello, L. E. Danielsen A. J. López-Tarrida, and J. R. Portillo, “The Lovász number as a physical limit of quantum correlations” (in preparation)

Cited in the paper.

Notice that G G is in general a vertex-weighted graph, since the probabilities of events may appear with different weights in the convex combination. For a weighted graph G G , definitions of α ⁡ ( G ) \alpha(G) , θ ⁡ ( G ) \theta(G) , and α ∗ ​ ( G ) \alpha^{*}(G) can be found in D. E. Knuth, “The sandwich theorem”, Electr. J. Comb. 1

Cited in the paper.

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

2011

Later among the works it cites.

S. Kochen (private communication, November 2012)

2012

Closest in time.