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Erschienen in:
Interpretations of QM with Applications for Formal Epistemology Kapitel lesen Erstes Kapitel lesen

2017 | OriginalPaper | Buchkapitel

On the Interpretation of Probabilities in Generalized Probabilistic Models

verfasst von : Federico Holik, Sebastian Fortin, Gustavo Bosyk, Angelo Plastino

Erschienen in: Quantum Interaction

Verlag: Springer International Publishing

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Abstract

We discuss generalized probabilistic models for which states not necessarily obey Kolmogorov’s axioms of probability. We study the relationship between properties and probabilistic measures in this setting, and explore some possible interpretations of these measures.

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Vorheriges Kapitel Exploration of Contextuality in a Psychophysical Double-Detection Experiment
Nächstes Kapitel An Introduction to Symmetric Inflated Probabilities
Fußnoten
1
An orthomodular lattice \(\mathcal {L}\), is defined as an orthocomplemented lattice satisfying that, for any a, b and c, if \(a\le c\), then \(a\vee (a^{\bot }\wedge c)=c\). In the Hilbert space case, projection operators are in one to one correspondence to closed subspaces. These form an orthomodular lattice with “\(\vee \)" representing the closure of the sum of two subspaces, “\(\wedge \)" its intersection, and “\((...)^{\bot }\)"representing the orthogonal complement of a given subspace. “\(\le \)" means subspace inclusion. See [23] for a detailed exposition.
 
2
It is important to notice here that different notions of “rational agent” could be used. In particular, it would be interesting to study the possibility of using Dutch Book Arguments in the generalized setting.
 
Literatur
1.
Bengtsson, I., Zyczkowski, K.: Geometry of Quantum States: An Introduction to Quantum Entanglement. Cambridge University Press, Cambridge (2006)CrossRefMATH
2.
Holik, F., Plastino, A., Saenz, M.: Natural information measures in Cox’ approach for contextual probabilistic theories. Quantum Inf. Comput. 16(1 & 2), 0115–0133 (2016)MathSciNet
3.
4.
5.
Gudder, S.P.: Stochastic Methods in Quantum Mechanics, North Holland, New York (1979)
6.
Dalla Chiara, M.L., Giuntini, R., Greechie, R.: Reasoning in Quantum Theory. Kluwer Academic Pubulisher, Dordrecht (2004)CrossRefMATH
7.
Rédei, M.: Quantum Logic in Algebraic Approach. Kluwer Academic Publishers, Dordrecht (1998)CrossRefMATH
8.
Rédei, M., Summers, S.: Studies in history and philosophy of science part B: studies in history and philosophy of modern physics. Probab. Quantum Mech. 38(2), 390–417 (2007)
9.
10.
11.
12.
13.
Kolmogorov, A.N.: Foundations of Probability Theory. Springer, Berlin (1933)MATH
14.
15.
Cox, R.T.: The Algebra of Probable Inference. The Johns Hopkins Press, Baltimore (1961)MATH
16.
Boole, G.: An Investigation of the Laws of Thought. Macmillan, London (1854)MATH
17.
Knuth, K.H.: Deriving laws from ordering relations. In: Erickson, G.J., Zhai, Y. (eds.) Proceedings of 23rd International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, American Institute of Physics, New York, NY, USA, pp. 204-235 (2004)
18.
Knuth, K.H. Measuring on lattices. In: Goggans, P., Chan, C.Y. (eds.) Proceedings of 23rd International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, American Institute of Physics, New York, NY, USA, Volume 707, pp. 132-144 (2004)
19.
Knuth, K.H.: Valuations on lattices and their application to information theory. In: Proceedings of the 2006 IEEE World Congress on Computational Intelligence, Vancouver, Canada, July 2006
20.
Knuth, K.H.: Lattice duality: the origin of probability and entropy. Neurocomputing 67C, 245–274 (2005)CrossRef
21.
22.
Goyal, P., Knuth, K.H., Skilling, J.: Origin of complex quantum amplitudes and Feynman’s rules. Phys. Rev. A 81, 022109 (2010)CrossRef
23.
Kalmbach, G.: Orthomodular Lattices. Academic Press, San Diego (1983)MATH
24.
Beltrametti, E.G., Cassinelli, G.: The Logic of Quantum Mechanics. Addison-Wesley, Reading (1981)MATH
25.
Reed, M., Simon, B.: Methods of modern mathematical physics I: functional analysis. Academic Press, New York (1972)MATH
26.
Holik, F., Massri, C., Plastino, A., Zuberman, L.: On the lattice structure of probability spaces in quantum mechanics. Int. J. Theor. Phys. 52(6), 1836–1876 (2013)MathSciNetCrossRefMATH
27.
Bub, J.: Quantum computation from a quantum logical perspective. Quant. Inf. Process. 7, 281–296 (2007)MathSciNetMATH
28.
Holik, F., Bosyk, G.M., Bellomo, G.: Quantum information as a non-kolmogorovian generalization of Shannon’s theory. Entropy 17, 7349–7373 (2015). doi:10.​3390/​e17117349 CrossRef
29.
Holik, F., Plastino, A., Mechanics, Q.: A new turn in probability theory. In: Zoheir, E. (ed.) Contemporary Research in Quantum Systems. Nova Publishers, New York (2014)
30.
Alfsen, E.M.: Compact Convex Sets and Boundary Integrals. Springer, Heidelberg (1971)CrossRefMATH
31.
Barnum, H., Duncan, R., Wilce, A.: Symmetry, compact closure and dagger compactness for categories of convex operational models. J. Philos. Logic 42, 501–523 (2013)MathSciNetCrossRefMATH
32.
Stubbe, I., Steirteghem, B.V.: Propositional systems, Hilbert lattices and generalized Hilbert spaces. In: Engesser, K., Gabbay, D.M., Lehmann, D. (eds.) Handbook Of Quantum Logic and Quantum Structures: Quantum Structures (2007)
33.
Barnum, H., Barret, J., Leifer, M., Wilce, A.: Generalized no-broadcasting theorem. Phys. Rev. Lett. 99, 240501 (2007)CrossRef
34.
Barnum, H., Wilce, A.: Information processing in convex operational theories. Electron. Not. Theor. Comput. Sci. 270(1), 3–15 (2011)CrossRefMATH
35.
Gleason, A.: Measures on the closed subspaces of a Hilbert space. J. Math. Mech. 6, 885–893 (1957)MathSciNetMATH
36.
37.
38.
Holik, F., Plastino, A., Saenz, M.: Natural information measures for contextual probabilistic models. Quantum Inf. Comput. 16(1 & 2), 0115–0133 (2016)MathSciNet
39.
40.
Svozil, K., Tkadlec, J.: Greechie diagrams, nonexistence of measures in quantum logics, and Kochen–Specker-type constructions. J. Math. Phys. 37, 5380–5401 (1996)MathSciNetCrossRefMATH
41.
Doring, A.: Kochen-Specker theorem for von neumann algebras. Int. J. Theor. Phys. 44(2) (2005)
42.
Smith, D.: Orthomodular Bell-Kochen-Specker theorem. Int. J. Theor. Phys. 43(10) (2004)
43.
44.
45.
46.
47.
Holik, F.: Logic, geometry and probability theory. SOP Trans. Thoer. Phys. 1, 128–137 (2014)CrossRef
48.
Halvorson, H., Müger, M.: Algebraic Quantum Field Theory. In: Butterfield, J.B., Earman, J.E. (eds.) Philosophy of Physics, Elsevier, Amsterdam, The Netherlands, pp. 731–922 (2006)
49.
50.
Bratteli, O., Robinson, D.W.: Operator Algebras and Quantum Statistical Mechanics: Volumes 1 and 2. Springer, Heidelberg (2012)
51.
Feynman, R.P.: The concept of probability in quantum mechanics. In: Proceedings of Second Berkeley Symposium on Mathethical Statistical and Probability, University of California Press, pp. 533–541 (1951)
52.
da Costa, N., Lombardi, O., Lastir, M.: A modal ontology of properties for quantum mechanics. Synthese 190(17), 3671–3693 (2013)MathSciNetCrossRefMATH
53.
Domenech, G., Holik, F., Massri, C.: A quantum logical and geometrical approach to the study of improper mixtures. J. Math. Phyys. 51(5), 052108 (2010)MathSciNetCrossRefMATH
Metadaten
Titel
On the Interpretation of Probabilities in Generalized Probabilistic Models
verfasst von
Federico Holik
Sebastian Fortin
Gustavo Bosyk
Angelo Plastino
Copyright-Jahr
2017
Buch
Quantum Interaction

Print ISBN: 978-3-319-52288-3

Electronic ISBN: 978-3-319-52289-0

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-3-319-52289-0_16