Please use this identifier to cite or link to this item: http://repositorio.ufla.br/jspui/handle/1/10804
Title: Estudo probabilístico de sistemas quânticos: relações entre desigualdades tipo Bell
Authors: Oliveira, Marcelo Silva de
Vera, José Alberto Casto Nogales
Souza, Devanil Jaques de
Chaves, Lucas Monteiro
Toppan, Francesco
Kuznetsova, Zhanna Gennadyevna
Leyva, Moisés Porfírio Rojas
Keywords: Axiomas de Kolmogorov
Desigualdades de Bell
Sistemas quânticos
Kolmogorov’s axioms
Bell’s inequalities
Quantum systems
Issue Date: 22-Jan-2016
Publisher: Universidade Federal de Lavras
Citation: VELOZO, F. A. Estudo probabilístico de sistemas quânticos: relações entre desigualdades tipo Bell. 2016. 172 p. Tese (Doutorado em Estatística e Experimentação Agrícola)-Universidade Federal de Lavras, Lavras, 2015.
Abstract: In 1964, John S. Bell publishes an article in response to the Einstein, Podolsky and Rosen paradox, in which he develops an inequality involving statistical correlation, basing on the supposition that Quantum Mechanics is a statistical theory. There should, therefore, exist a random variable related to the observations, in which, if there was the possibility of knowing its value, the result of the experiment would be completely predictable. Thus, the lack of predictability of the experiment would be due to the ignorance regarding the value that such variable assumes during the experiment. However, when using the formula obtained by calculating the probabilities of the Quantum Mechanic experiment, we find a set of values in which the inequality is violated. Thus, we concluded that the Kolmogorov probability axioms are not enough to describe quantum phenomena. In 1969, J. F. Clauser, M. A. Horne, A. Shimony and R. A. Holt adapted Bell’s inequality for a viable experiment. In this dissertation, we compared the violation regions of the Wigner and Bell inequalities, verifying that they are equal and equivalent to the violation of one of the Kolmogorov axioms. We also verified that it is possible to create probability functions for quantum experiments that represent the Bell and Clauser-Horne-Shimony-Holt inequalities if compatible for changing a Kolmogorov axiom. The dissertation aims at regarding a few incompatibilities of the Quantum Theory with the Probability Theory found in literature, statistically analyzing the formulas obtained.
URI: http://repositorio.ufla.br/jspui/handle/1/10804
Appears in Collections:Estatística e Experimentação Agropecuária - Doutorado (Teses)



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