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Abstract:

We study improper mixtures from a quantum logical and geometrical point of view. Taking into account the fact that improper mixtures do not admit an ignorance interpretation and must be considered as states in their own right, we do not follow the standard approach which considers improper mixtures as measures over the algebra of projections. Instead of it, we use the convex set of states in order to construct a new lattice whose atoms are all physical states: pure states and improper mixtures. This is done in order to overcome one of the problems which appear in the standard quantum logical formalism, namely, that for a subsystem of a larger system in an entangled state, the conjunction of all actual properties of the subsystem does not yield its actual state. In fact, its state is an improper mixture and cannot be represented in the von Neumann lattice as a minimal property which determines all other properties as is the case for pure states or classical systems. The new lattice also contains all propositions of the von Neumann lattice. We argue that this extension expresses in an algebraic form the fact that-alike the classical case-quantum interactions produce nontrivial correlations between the systems. Finally, we study the maps which can be defined between the extended lattice of a compound system and the lattices of its subsystems. © 2010 American Institute of Physics.

Registro:

Documento: Artículo
Título:A quantum logical and geometrical approach to the study of improper mixtures
Autor:Domenech, G.; Holik, F.; Massri, C.
Filiación:Instituto de Astronomía y Física del Espacio (IAFE), Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires, Argentina
Departamento de Matemática-Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I (C1428EGA), Buenos Aires, Argentina
Año:2010
Volumen:51
Número:5
DOI: http://dx.doi.org/10.1063/1.3429619
Título revista:Journal of Mathematical Physics
Título revista abreviado:J. Math. Phys.
ISSN:00222488
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00222488_v51_n5_p_Domenech.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222488_v51_n5_p_Domenech

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Citas:

---------- APA ----------
Domenech, G., Holik, F. & Massri, C. (2010) . A quantum logical and geometrical approach to the study of improper mixtures. Journal of Mathematical Physics, 51(5).
http://dx.doi.org/10.1063/1.3429619
---------- CHICAGO ----------
Domenech, G., Holik, F., Massri, C. "A quantum logical and geometrical approach to the study of improper mixtures" . Journal of Mathematical Physics 51, no. 5 (2010).
http://dx.doi.org/10.1063/1.3429619
---------- MLA ----------
Domenech, G., Holik, F., Massri, C. "A quantum logical and geometrical approach to the study of improper mixtures" . Journal of Mathematical Physics, vol. 51, no. 5, 2010.
http://dx.doi.org/10.1063/1.3429619
---------- VANCOUVER ----------
Domenech, G., Holik, F., Massri, C. A quantum logical and geometrical approach to the study of improper mixtures. J. Math. Phys. 2010;51(5).
http://dx.doi.org/10.1063/1.3429619