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I discuss a set of strong, but probabilistically intelligible, axioms from which one can {\em almost} derive the appratus of finite dimensional quantum theory.
Birkhoff and von Neumann, The logic of quantum mechanics, Annals of Math., 37
1936
Earlier work this paper cites.
J. von Neumann, Mathematical Foundations of Quantum Mechnanics
1952
Earlier work this paper cites.
M. Koecher, Die geoodätischen von positivitaätsbereichen, Math. Annalen 135
1958
Earlier work this paper cites.
E. B. Vinberg, Homogeneous cones, Dokl. Acad. Nauk. SSSR 141
1961
Earlier work this paper cites.
N. Zierler, Axioms for non-relativistic quantum mechanics, Pacific Journal of Mathematics 11
1961
Earlier work this paper cites.
G. Mackey, Mathematical Foundations of Quantum Mechanics
1963
Earlier work this paper cites.
J. Gunson, On the algebraic structure of Quantum Mechanics, Comm. Math. Phys. 6
1967
Earlier work this paper cites.
B. Mielnik, Theory of filters, Comm. Math. Phys. 15
1969
Earlier work this paper cites.
J. Bellisard and B. Iochum, Homogeneous self-dual cones, versus Jordan algebras. The theory revisited. Ann. Inst. Fourier, Grenoble 28
1978
Earlier work this paper cites.
H. Araki, On a characterization of the state space of quantum mechanics, Comm. Math. Phys. 75
1980
Cited alongside, same era.
D. J. Foulis and C. H. Randall, An approach to empirical logic, American Math. Monthly 77
1981
Cited alongside, same era.
H. Hanche-Olsen, Jordan algebras with tensor products are C* algebras, Springer Lecture Notes in Mathematics 1132, Springer Verlag, 1985, pp. 223-229
1985
Cited alongside, same era.
M. Kläy, C. H. Randall and D. J. Foulis, Tensor products and probability weights, Int. J. Theor. Phys
1987
Cited alongside, same era.
G. Ludwig, An Axiomatic Basis for Quantum Mechanics
1987
Cited alongside, same era.
E. B. Vingerg, Linear Representations of Groups
1989
H. Barnum, J. Barrett, M. Leifer and A. Wilce, Cloning and broadcasting in generic probabilistic theories, arXiv: 0611295; also A general no-broadcasting theorem, Phys. Rev. Lett. 99
2007
Later among the works it cites.
P. Goyal, Information-theoretic approach to quantum theory, I: the abstract quantum formalism, quant-ph/0702124v1 (2007)
2007
Later among the works it cites.
J. Rau, On quantum vs. classical probability, arXiv:0710.2119v1, 2007
2007
Later among the works it cites.
2008
Later among the works it cites.
G. M. D’Ariano, Probabilistic theories: what is special about quantum mechanics?, ArXiv: 0807.438, 2008
2008
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Cited alongside, same era.
H. Kummer, A constructive approach to the foundations of quantum mechanics, Foundations of Physics 17
1991
Cited alongside, same era.
L. Hardy, Quantum theory from five reasonable axioms, arXiv: quant-ph/00101012 (2001)
2001
Cited alongside, same era.
S. Abramsky and B. Coecke, A categorical semantics of quantum protocols, Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science (2004), 415-425 (arXiv: quant-ph/0402130)
2004
Cited alongside, same era.
H. Barnum, C. P. Gaebbler and A. Wilce, Ensemble steering, weak self-duality, and the structure of probabilistic theories, in preparation
Cited in the paper.
J. Barrett, Information processing in general probabilistic theories, arXiv:quant-ph/0508211
Cited in the paper.
C. Piron, Axiomatique Quantique
Cited in the paper.
Later among the works it cites.
Quan Tran and A. Wilce, Covariance in quantum logic, Int. J. ther. Phys. 47
2008
Later among the works it cites.
2009
Closest in time.
A. Wilce, Test spaces, in D. Gabbay, K. Engesser and D. Lehman, Handbook of Quantum Logic
2009
Closest in time.