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Ontological models are attempts to quantitatively describe the results of a probabilistic theory, such as Quantum Mechanics, in a framework exhibiting an explicit realism-based underpinning.
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1955
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J. S. Bell, “On the Problem of Hidden Variables in Quantum Mechanics”, Rev. Mod. Phys. 38
1966
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S. Kochen and E. Specker, “The Problem of Hidden Variables in Quantum Mechanics”, Journal of Mathematics and Mechanics 17
1967
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M. Kernaghan, “Bell-Kochen-Specker Theorem for 20 Vectors”, J. Phys. A 27
1994
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E. G. Beltrametti and S. Bugajski, “A Classical Extension of Quantum Mechanics”, J. Phys. A: Math. Gen., 28
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R. A. Horn and C. R. Johnson, Matrix Analysis
1999
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D. D. Lee and H. S. Seung, “ Learning the parts of objects by non-negative matrix factorization”, Nature 401
1999
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A. Berman and N. Shaked-Monderer, Completely positive matrices
2003
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F. Barioli and A. Berman, “The maximal cp-rank of rank k completely positive matrices”, Linear Algebra Appl. 363
2003
Cited alongside, same era.
P. G. L. Mana, “Why can states and measurement outcomes be represented as vectors?”, quant-ph/0305117v3 (2004)
2004
Cited alongside, same era.
K. S. Gibbons, M. J. Hoffman and W. K. Wootters, “ Discrete phase space based on finite fields”, Phys. Rev. A. 70
2004
Cited alongside, same era.
L. Hardy, “Quantum Ontological Excess Baggage”, Stud. Hist. Philos. M. P. 35B
S. Aaronson, “Quantum Computing and Hidden Variables”, Phys. Rev. A 71
2005
Later among the works it cites.
R. W. Spekkens, “Contextuality for preparations, transformations, and unsharp measurements”, Phys. Rev. A 71
2005
Later among the works it cites.
S. Aaronson, “Limitations of quantum advice and one-way communication”, Theor. comput. 1
2005
Later among the works it cites.
H. Barnum, J. Barrett, M. Leifer, A. Wilce, “Cloning and Broadcasting in Generic Probabilistic Theories”, quant-ph/0611295v1 (2006)
2006
Later among the works it cites.
J. Barrett, “Information Processing in Generalized Probabilistic Theories”, Phys. Rev. A 75
2007
Closest in time.
N.-D. Ho and P. van Dooren, Non-negative matrix factorizations with fixed row and column sums, Preprint (2007)
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2004
Cited alongside, same era.
R. Spekkens, “In defense of the epistemic view of quantum states: a toy theory”, quant-ph/0401052 v1 (to be published)
Cited in the paper.
L. Hardy, “Quantum Theory from Five Reasonable Axioms”, quant-ph/0101012
Cited in the paper.
N. Harrigan, T. Rudolph and R. Spekkens, “Contextuality in the Ontological Model Formalism”. This paper is completed, but for months has been awaiting Dr. Spekkens’ final approval. Please email him and ask him for a copy: r.w.spekkens@damtp.cam.ac.uk
Cited in the paper.
R. W. Spekkens, private communication
Cited in the paper.
N. Harrigan, R. Spekkens, “Einstein and the Epistemic View of Quantum States”, arXiv:0706.2661v1
Cited in the paper.
T. Rudolph “Ontological models for Quantum Mechanics and the Kochen Specker theorem”, quant-ph/0608120 v1
Cited in the paper.
2007
Closest in time.