Navegar

Colección

Datos Estadísticas

Artículo

Holik, F.; Massri, C.; Plastino, A.; Zuberman, L. "On the Lattice Structure of Probability Spaces in Quantum Mechanics" (2013) International Journal of Theoretical Physics. 52(6):1836-1876
La versión final de este artículo es de uso interno. El editor solo permite incluir en el repositorio el artículo en su versión post-print. Por favor, si usted la posee enviela a
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

Let C be the set of all possible quantum states. We study the convex subsets of C with attention focused on the lattice theoretical structure of these convex subsets and, as a result, find a framework capable of unifying several aspects of quantum mechanics, including entanglement and Jaynes' Max-Ent principle. We also encounter links with entanglement witnesses, which leads to a new separability criteria expressed in lattice language. We also provide an extension of a separability criteria based on convex polytopes to the infinite dimensional case and show that it reveals interesting facets concerning the geometrical structure of the convex subsets. It is seen that the above mentioned framework is also capable of generalization to any statistical theory via the so-called convex operational models' approach. In particular, we show how to extend the geometrical structure underlying entanglement to any statistical model, an extension which may be useful for studying correlations in different generalizations of quantum mechanics. © 2012 Springer Science+Business Media, LLC.

Registro:

Documento: Artículo
Título:On the Lattice Structure of Probability Spaces in Quantum Mechanics
Autor:Holik, F.; Massri, C.; Plastino, A.; Zuberman, L.
Filiación:Instituto de Física (IFLP-CCT-CONICET), Universidad Nacional de La Plata, C.C. 727, 1900 La Plata, Argentina
Departamento de Matemática - Facultad de Ciencias Exactas y Naturales, Becario CONICET, Universidad de Buenos Aires - Pabellón I, Ciudad Universitaria, Buenos Aires, Argentina
IFISC (CSIC-UIB), Campus Universitat Illes Balears, 07122 Palma de Mallorca, Spain
Departamento de Matemática - Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires - Pabellón I, Ciudad Universitaria, Buenos Aires, Argentina
Palabras clave:Convex sets; Entanglement; MaxEnt approach; Quantum information
Año:2013
Volumen:52
Número:6
Página de inicio:1836
Página de fin:1876
DOI: http://dx.doi.org/10.1007/s10773-012-1277-5
Título revista:International Journal of Theoretical Physics
Título revista abreviado:Int. J. Theor. Phys.
ISSN:00207748
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00207748_v52_n6_p1836_Holik

Referencias:

  • Stulpe, W., Swat, M., (2001) Found. Phys. Lett., 14, p. 285
  • Barnum, H., Barret, J., Leifer, M., Wilce, A., (2007) Phys. Rev. Lett., 99. , 240501
  • Barnum, H., Wilce, A., (2009), arXiv: 0908. 2352v1 [quant-ph]; Barnum, H., Wilce, A., (2011) Electron. Notes Theor. Comput. Sci., 270 (1), pp. 3-15
  • Barnum, H., Duncan, R., Wilce, A., (2010), arXiv: 1004. 2920v1 [quant-ph]; Beltrametti, E., Bugajski, S., Varadarajan, V., (2000) J. Math. Phys., 41, p. 2500
  • Gudder, S.P., (1979) Stochastic Methods in Quantum Mechanics, pp. 6-34. , New York: North-Holland
  • Cattaneo, G., Gudder, S., (1999) Found. Phys., 29
  • Mielnik, B., (1968) Commun. Math. Phys., 9, pp. 55-80
  • Mielnik, B., (1969) Commun. Math. Phys., 15, pp. 1-46
  • Mielnik, B., (1974) Commun. Math. Phys., 37, pp. 221-256
  • Birkhoff, G., von Neumann, J., (1936) Ann. Math., 37, pp. 823-843
  • Putnam, H., Is logic empirical? (1968) Boston Studies in the Philosophy of Science, 5, pp. 216-241. , R. S. Cohen and M. W. Wartofsky (Eds.), Dordrecht: Reidel
  • Mackey, G.W., (1957) Am. Math. Mon., 64 (SUPPL.), pp. 45-57
  • Jauch, J.M., (1968) Foundations of Quantum Mechanics, , Cambridge: Addison-Wesley
  • Piron, C., (1976) Foundations of Quantum Physics, , Cambridge: Addison-Wesley
  • Kalmbach, G., (1983) Orthomodular Lattices, , San Diego: Academic Press
  • Kalmbach, G., (1986) Measures and Hilbert Lattices, , Singapore: World Scientific
  • Varadarajan, V., (1968) Geometry of Quantum Theory I, , Princeton: Van Nostrand
  • Varadarajan, V., (1970) Geometry of Quantum Theory II, , Princeton: Van Nostrand
  • Greechie, J.R., (1981) Current Issues in Quantum Logic, pp. 375-380. , E. Beltrameti and B. Fraassenvan (Eds.), New York: Plenum
  • Gudder, S.P., (1978) Mathematical Foundations of Quantum Theory, , A. R. Marlow (Ed.), New York: Academic Press
  • Giuntini, R., (1991) Quantum Logic and Hidden Variables, , Mannheim: BI Wissenschaftsverlag
  • Pták, P., Pulmannova, S., (1991) Orthomodular Structures as Quantum Logics, , Dordrecht: Kluwer Academic
  • Beltrametti, E.G., Cassinelli, G., (1981) The Logic of Quantum Mechanics, , Reading: Addison-Wesley
  • Dalla Chiara, M.L., Giuntini, R., Greechie, R., (2004) Reasoning in Quantum Theory, , Dordrecht: Kluwer Academic
  • Dvurečenskij, A., Pulmannová, S., (2000) New Trends in Quantum Structures, , Dordrecht: Kluwer Academic
  • Engesser, K., Gabbay, D.M., Lehmann, D., (2009) Handbook of Quantum Logic and Quantum Structures (Quantum Logic), , Amsterdam: North-Holland
  • Aerts, D., Daubechies, I., (1979) Lett. Math. Phys., 3, pp. 11-17
  • Aerts, D., Daubechies, I., (1979) Lett. Math. Phys., 3, pp. 19-27
  • Randall, C.H., Foulis, D.J., (1981) Interpretation and Foundations of Quantum Theory, pp. 21-28. , H. Neumann (Ed.), Mannheim: Bibliographisches Institut
  • Domenech, G., Holik, F., Massri, C., (2010) J. Math. Phys., 51. , 052108
  • Holik, F., Massri, C., Ciancaglini, N., (2012) Int. J. Theor. Phys., 51 (5), pp. 1600-1620. , doi:10.1007/s10773-011-1037-y
  • Jaynes, E.T., (1957) Phys. Rev., 106 (4), pp. 620-630
  • Jaynes, E.T., (1957) Phys. Rev., 108 (2), pp. 171-190
  • Holik, F., Plastino, A., (2012) J. Math. Phys., 53. , 073301, doi:10.1063/1.4731769
  • Holik, F., Massri, C., Plastino, A., (2012), arXiv: 1202. 0679v1; Holik, F., Plastino, A., (2011) Phys. Rev. A, 84. , 062327
  • Clifton, R., Halvorson, H., (1999) Phys. Rev. A, 61. , 012108
  • Clifton, R., Halvorson, H., Kent, A., (2000) Phys. Rev. A, 61. , 042101
  • Zyczkowski, K., Horodecki, P., Sanpera, A., Lewenstein, M., (1998) Phys. Rev. A, 58, p. 883
  • Reed, M., Simon, B., (1972) Methods of Modern Mathematical Physics I: Functional Analysis, , New York: Academic Press
  • Rédei, M., (1998) Quantum Logic in Algebraic Approach, , Dordrecht: Kluwer Academic
  • Wilce, A., Quantum Logic and Probability Theory (2009) The Stanford Encyclopedia of Philosophy, , http://plato.stanford.edu/archives/spr2009/entries/qt-quantlog/, (Spring, 2009 edn.), Zalta, E. N. (ed.), Archive edition: Spring
  • Gleason, A., (1957) J. Math. Mech., 6, pp. 885-893
  • Buhagiar, D., Chetcuti, E., Dvurečenskij, A., (2009) Found. Phys., 39, pp. 550-558
  • Busch, P., Kiukas, J., Lahti, P., (2009), arXiv: 0905. 3222v1 [quant-ph]; Heinonen, T., (2005) Imprecise measurements in quantum mechanics, , Ph. D. thesis
  • Ma, Z., (2008), arXiv: 0811. 2454v1 [quant-ph]; Foulis, D., Gudder, S., (2001) Found. Phys., 31, pp. 1515-1544
  • Werner, R., (1989) Phys. Rev. A, 40, pp. 4277-4281
  • Bengtsson, I., Zyczkowski, K., (2006) Geometry of Quantum States: An Introduction to Quantum Entanglement, , Cambridge: Cambridge University Press
  • Horodecki, M., Horodecki, P., Horodecki, R., (2001) Quantum Information, 173, p. 151. , Springer Tracts in Modern Physics, G. Alber (Ed.), Berlin: Springer
  • Aubrun, G., Szarek, S., (2006) Phys. Rev. A, 73. , 022109
  • Schlosshauer, M., (2007) Decoherence and the Quantum-to-Classical Transition, , New York: Springer
  • Castagnino, M., Fortin, S., (2011) Int. J. Theor. Phys., 50 (7), pp. 2259-2267
  • Castagnino, M., (2008) Class. Quantum Gravity, 25. , 154002
  • D'Espagnat, D., (1976) Conceptual Foundations of Quantum Mechanics, , Reading: Benjaming
  • Kirkpatrik, K.A., (2001), arXiv: quant-ph/0109146v2. 21 October; D'Espagnat, D., (2001), arXiv: quant-ph/0111081v1. 14 November; Bratteli, O., Robinson, D., (1979) Operator Algebras and Quantum Statistical Mechanics I, , New York: Springer
  • Holevo, A., Shirokov, M., Werner, R., (2005) Russ. Math. Surv., 60 (2), pp. 153-154. , arXiv:quant-ph/0504204
  • Rockafellar, T., (1972) Convex Analysis
  • Horodeki, R., Horodki, P., Horodeki, M., Horodeki, K., (2009) Rev. Mod. Phys., 81, pp. 865-942
  • Massri, C., Algorithm to find maximum of a multilinear map over a product of spheres, , http://arxiv.org/abs/1110.6217
  • Brezis, H., (1987) Analyse Fonctionnelle
  • Valentine, F., (1964) Convex Sets, , New York: McGraw-Hill

Citas:

---------- APA ----------
Holik, F., Massri, C., Plastino, A. & Zuberman, L. (2013) . On the Lattice Structure of Probability Spaces in Quantum Mechanics. International Journal of Theoretical Physics, 52(6), 1836-1876.
http://dx.doi.org/10.1007/s10773-012-1277-5
---------- CHICAGO ----------
Holik, F., Massri, C., Plastino, A., Zuberman, L. "On the Lattice Structure of Probability Spaces in Quantum Mechanics" . International Journal of Theoretical Physics 52, no. 6 (2013) : 1836-1876.
http://dx.doi.org/10.1007/s10773-012-1277-5
---------- MLA ----------
Holik, F., Massri, C., Plastino, A., Zuberman, L. "On the Lattice Structure of Probability Spaces in Quantum Mechanics" . International Journal of Theoretical Physics, vol. 52, no. 6, 2013, pp. 1836-1876.
http://dx.doi.org/10.1007/s10773-012-1277-5
---------- VANCOUVER ----------
Holik, F., Massri, C., Plastino, A., Zuberman, L. On the Lattice Structure of Probability Spaces in Quantum Mechanics. Int. J. Theor. Phys. 2013;52(6):1836-1876.
http://dx.doi.org/10.1007/s10773-012-1277-5