Abstract:
In this paper we develop an algebraic framework in which several classes of two-valued states over orthomodular lattices may be equationally characterized. The class of two-valued states and the subclass of Jauch-Piron two-valued states are among the classes which we study. © 2011 Polish Scientific Publishers.
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Documento: |
Artículo
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Título: | Equational characterization for two-valued states in orthomodular quantum systems |
Autor: | Domenech, G.; Freytes, H.; de Ronde, C. |
Filiación: | Instituto de Astronomía y Física del Espacio (IAFE) Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires, Argentina Universita degli Studi di Cagliari, Via Is Mirrionis 1, 09123 Cagliari, Italy Instituto Argentino de Matemática (IAM), Saavedra 15 - 3er piso, 1083 Buenos Aires, Argentina Center Leo Apostel (CLEA), Belgium Foundations of the Exact Sciences (FUND) Brussels Free University Krijgskundestraat 33, 1160 Brussels, Belgium
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Palabras clave: | Orthomodular lattices; Two-valued states; Varieties |
Año: | 2011
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Volumen: | 68
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Número: | 1
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Página de inicio: | 65
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Página de fin: | 83
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DOI: |
http://dx.doi.org/10.1016/S0034-4877(11)60027-X |
Título revista: | Reports on Mathematical Physics
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Título revista abreviado: | Rep. Math. Phys.
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ISSN: | 00344877
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CODEN: | RMHPB
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00344877_v68_n1_p65_Domenech |
Referencias:
- Bell, J.S., On the Einstein-Podolsky-Rosen paradox (1964) Physics, 1, pp. 195-200
- Birkhoff, G., von Neumann, J., The logic of quantum mechanics (1936) Ann. Math., 27, pp. 823-843
- Bohm, D., A suggested interpretations of the quantum theory in therms of 'hidden variables': Part I (1952) Phys. Rev., 85, pp. 166-179
- Burris, S., Sankappanavar, H.P., (1981) A Course in Universal, Graduate Text in Mathematics, 78. , Springer, New York-Heidelberg-Berlin
- Dalla Chiara, M.L., Giuntini, R., Greechie, R., (2004) Reasoning in Quantum Theory, Sharp and Unsharp Quantum Logics, , Kluwer, Dordrecht-Boston-London
- Di Nola, A., Dvurecenskij, A., Lettieri, A., (2009), On varieties of MV-algebras with internal states, Int. J. Approx. Reasoning (to appear); Dvurecenskij, A., (2009), On States on MV-algebras and their Applications, J. Logic and Computation (to appear); Einstein, A., Rosen, P.A.N., Can Quantum-Mechanical Description be Considered Complete? (1935) Phys. Rev., 47, pp. 777-780
- Foulis, D., Observables, states, and symmetries in the context of CB-effect algebras (2007) Rep. Math. Phys., 60, pp. 329-346
- Godowski, R., Varieties of orthomodular lattices with strongly full set of states (1982) Demostratio Math., 60 (3), pp. 725-732
- Gudder, S., (1979) Stochastic Methods in Quantum Mechanics, , Elseiver-North-Holand, New York
- Jauch, J., (1968) Foundations of Quantum Mechanics, , Addison Wesley, Reading, Mass
- Kalman, J.A., Lattices with involution (1958) Trans. Amer. Math. Soc., 87, pp. 485-491
- Kalmbach, G., (1983) Ortomodular Lattices, , Academic Press, London
- Kühr, J., Mundici, D., De Finetti theorem and Borel states in [0, 1]-valued logic (2007) Int. J. Approx. Reason, 46 (3), pp. 605-616
- Kroupa, T., Every state on semisimple MV-algebra is integral (2006) Fuzzy Sets Syst., 157, pp. 2771-2787
- Flaminio, T., Montagna, F., MV-algebras with internal states and probabilistic fuzzy logics (2009) Int. J. Approx. Reas., 50, pp. 138-152
- Harding, J., Pták, P., On the set representation of an orthomodular poset (2001) Colloquium Math., 89, pp. 233-240
- Maeda, F., Maeda, S., (1970) Theory of Symmetric Lattices, , Springer, Berlin
- Mayet, R., Varieties of orthomodular lattices related to states (1985) Algebra Universalis, 20, pp. 368-396
- Navara, M., Descriptions of states spaces of orthomodular lattices (1992) Math. Bohemica, 117, pp. 305-313
- Navara, M., Triangular norms and measure of fuzzy set (2005) Logical, Algebraic, Analytic and Probabilistic Aspect of Triangular Norms, pp. 345-390. , Elsevier, Amsterdan
- von Neumann, J., (1996) Mathematical Foundations of Quantum Mechanics, , Princeton University Press, Princeton
- Piron, C., (1964) Helv. Phys. Acta, 37, p. 439
- Piron, C., (1976) Foundations of Quantum Physics, , Benjamin, Reading, Mass
- Pták, P., Pulmannová, S., (1991) Orthomodular Structures as Quantum Logics, , Kluwer, Dordrecht
- Pulmannová, S., Sharp and unsharp observables on s-MV algebras A comparison with the Hilbert space approach (2008) Fuzzy Sets Syst., 159 (22), pp. 3065-3077
- Pták, P., Weak dispersion-free states and hidden variables hypothesis (1983) J. Math. Phys., 24, pp. 839-840
- Riecanová, Z., Continuous lattice effect algebras admitting order-continuous states (2003) Fuzzy Sets Syst., 136, pp. 41-54
- Riecanová, Z., Effect algebraic extensions of generalized effect algebras and two-valued states (2008) Fuzzy Sets Syst., 159, pp. 1116-1122
- Rüttimann, G.T., Jauch-Piron states (1977) J. Math. Phys., 18, pp. 189-193
- Tkadlec, J., Partially additive measures and set representation of orthoposets (1993) J. Pure Appl. Algebra, 86, pp. 79-94
- Tkadlec, J., Partially additive states on orthomodular posets (1995) Colloquium Math., 62, pp. 7-14
- Tkadlec, J., Boolean orthoposets and two-valued states on them" (1992) Rep. Math. Phys., 31, pp. 311-316
Citas:
---------- APA ----------
Domenech, G., Freytes, H. & de Ronde, C.
(2011)
. Equational characterization for two-valued states in orthomodular quantum systems. Reports on Mathematical Physics, 68(1), 65-83.
http://dx.doi.org/10.1016/S0034-4877(11)60027-X---------- CHICAGO ----------
Domenech, G., Freytes, H., de Ronde, C.
"Equational characterization for two-valued states in orthomodular quantum systems"
. Reports on Mathematical Physics 68, no. 1
(2011) : 65-83.
http://dx.doi.org/10.1016/S0034-4877(11)60027-X---------- MLA ----------
Domenech, G., Freytes, H., de Ronde, C.
"Equational characterization for two-valued states in orthomodular quantum systems"
. Reports on Mathematical Physics, vol. 68, no. 1, 2011, pp. 65-83.
http://dx.doi.org/10.1016/S0034-4877(11)60027-X---------- VANCOUVER ----------
Domenech, G., Freytes, H., de Ronde, C. Equational characterization for two-valued states in orthomodular quantum systems. Rep. Math. Phys. 2011;68(1):65-83.
http://dx.doi.org/10.1016/S0034-4877(11)60027-X