Relativistic symmetry in quantum information theory

Detalhes bibliográficos
Ano de defesa: 2022
Autor(a) principal: Bidinotto, Alexandre Borges lattes
Orientador(a): Avelar, Ardiley Torres lattes
Banca de defesa: Avelar, Ardiley Torres, Santana, Ademir Eugênio de, Cardoso, Wesley Bueno
Tipo de documento: Dissertação
Tipo de acesso: Acesso aberto
Idioma: eng
Instituição de defesa: Universidade Federal de Goiás
Programa de Pós-Graduação: Programa de Pós-graduação em Fisica (IF)
Departamento: Instituto de Física - IF (RG)
País: Brasil
Palavras-chave em Português:
Simetria
Teoria de grupos
Relatividade restrita
Tomografia de estados quânticos
Palavras-chave em Inglês:
Symmetry
Group theory
Special relativity
Quantum state tomography
Área do conhecimento CNPq:
CIENCIAS EXATAS E DA TERRA::FISICA
Link de acesso: http://repositorio.bc.ufg.br/tede/handle/tede/12039
Resumo: This dissertation begins with a succinct introduction to group theory to enable the understanding of special relativity theory from a symmetrical point of view. From this perspective, the notion of hierarchy of dynamical variables, which is present in relativity, is introduced to quantum mechanical formalism in order to construct the irreducible unitary representations of the Poincaré group for secondary variables. Given this discussion, the questions regarding the existence of a subset of transformations in which the Wigner rotations associated do not depend on the momenta. In sequence, the relativistic Stern-Gerlach observable is presented. This observable also depends on the momenta, so the initial problem on the density matrices for spin remains unsolved. The open question on the Stern-Gerlach observable is what is the minimum number of measurements in order to fully determine a relativistic density matrix. Both questionings on this dissertation can lead to the determination of the quantum state tomography of relativistic particles, which is the further goal of this document.
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spelling Avelar, Ardiley Torreshttp://lattes.cnpq.br/5732286631137637Taillebois, Emile Raymond FerreiraAvelar, Ardiley TorresSantana, Ademir Eugênio deCardoso, Wesley Buenohttp://lattes.cnpq.br/6736689883670342Bidinotto, Alexandre Borges2022-05-04T15:40:15Z2022-05-04T15:40:15Z2022-04-04BIDINOTTO, A. B. Relativistic symmetry in quantum information theory. 2022. 49 f. Dissertação (Mestrado em Física) - Universidade Federal de Goiás, Goiânia, 2022.http://repositorio.bc.ufg.br/tede/handle/tede/12039This dissertation begins with a succinct introduction to group theory to enable the understanding of special relativity theory from a symmetrical point of view. From this perspective, the notion of hierarchy of dynamical variables, which is present in relativity, is introduced to quantum mechanical formalism in order to construct the irreducible unitary representations of the Poincaré group for secondary variables. Given this discussion, the questions regarding the existence of a subset of transformations in which the Wigner rotations associated do not depend on the momenta. In sequence, the relativistic Stern-Gerlach observable is presented. This observable also depends on the momenta, so the initial problem on the density matrices for spin remains unsolved. The open question on the Stern-Gerlach observable is what is the minimum number of measurements in order to fully determine a relativistic density matrix. Both questionings on this dissertation can lead to the determination of the quantum state tomography of relativistic particles, which is the further goal of this document.Esta dissertação começa com uma introdução sucinta à teoria dos grupos para permitir a compreensão da teoria da relatividade especial de um ponto de vista simétrico. Nessa perspectiva, a noção de hierarquia de variáveis dinâmicas, que está presente na relatividade, é introduzida no formalismo da mecânica quântica a fim de construir as representações unitárias irredutíveis do grupo de Poincaré para variáveis secundárias. Diante dessa discussão, questiona-se a existência de um subconjunto de transformações em que as rotações de Wigner associadas independem dos momentos. Em sequência, o observável do experimento de Stern-Gerlach relativístico é apresentado. Este observável também depende dos momentos, então o problema inicial nas matrizes de densidade para spin permanece. A questão em aberto no observável Stern-Gerlach é: Qual é o número mínimo de medições para determinar completamente uma matriz de densidade relativística? Ambos os questionamentos desta dissertação podem levar à determinação da tomografia de estados quânticos de partículas relativísticas, que é o objetivo futuro deste documento.Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPqengUniversidade Federal de GoiásPrograma de Pós-graduação em Fisica (IF)UFGBrasilInstituto de Física - IF (RG)Attribution-NonCommercial-NoDerivatives 4.0 Internationalinfo:eu-repo/semantics/openAccessSimetriaTeoria de gruposRelatividade restritaTomografia de estados quânticosSymmetryGroup theorySpecial relativityQuantum state tomographyCIENCIAS EXATAS E DA TERRA::FISICARelativistic symmetry in quantum information theorySimetria relativística na teoria de informação quânticainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesis57500500500500251850reponame:Repositório Institucional da UFGinstname:Universidade Federal de Goiás (UFG)instacron:UFGCC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805http://repositorio.bc.ufg.br/tede/bitstreams/c1f19992-8e98-4938-8d67-1316fcdf447d/download4460e5956bc1d1639be9ae6146a50347MD52ORIGINALDissertação - Alexandre Borges Bidinotto - 2022.pdfDissertação - Alexandre Borges Bidinotto - 2022.pdfapplication/pdf951086http://repositorio.bc.ufg.br/tede/bitstreams/4f8762e4-9336-477d-b59c-e478f4be7f4c/downloadf98137b7a043617e7cda05ed1460e2a9MD53LICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://repositorio.bc.ufg.br/tede/bitstreams/aa207a07-166b-44e4-8b1a-57ac9d86e5c5/download8a4605be74aa9ea9d79846c1fba20a33MD54tede/120392022-05-04 12:40:15.595http://creativecommons.org/licenses/by-nc-nd/4.0/Attribution-NonCommercial-NoDerivatives 4.0 Internationalopen.accessoai:repositorio.bc.ufg.br:tede/12039http://repositorio.bc.ufg.br/tedeRepositório InstitucionalPUBhttps://repositorio.bc.ufg.br/tedeserver/oai/requestgrt.bc@ufg.bropendoar:oai:repositorio.bc.ufg.br:tede/12342022-05-04T15:40:15Repositório Institucional da UFG - Universidade Federal de Goiás (UFG)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
dc.title.pt_BR.fl_str_mv Relativistic symmetry in quantum information theory
dc.title.alternative.por.fl_str_mv Simetria relativística na teoria de informação quântica
title Relativistic symmetry in quantum information theory
spellingShingle Relativistic symmetry in quantum information theory
Bidinotto, Alexandre Borges
Simetria
Teoria de grupos
Relatividade restrita
Tomografia de estados quânticos
Symmetry
Group theory
Special relativity
Quantum state tomography
CIENCIAS EXATAS E DA TERRA::FISICA
title_short Relativistic symmetry in quantum information theory
title_full Relativistic symmetry in quantum information theory
title_fullStr Relativistic symmetry in quantum information theory
title_full_unstemmed Relativistic symmetry in quantum information theory
title_sort Relativistic symmetry in quantum information theory
author Bidinotto, Alexandre Borges
author_facet Bidinotto, Alexandre Borges
author_role author
dc.contributor.advisor1.fl_str_mv Avelar, Ardiley Torres
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/5732286631137637
dc.contributor.advisor-co1.fl_str_mv Taillebois, Emile Raymond Ferreira
dc.contributor.referee1.fl_str_mv Avelar, Ardiley Torres
dc.contributor.referee2.fl_str_mv Santana, Ademir Eugênio de
dc.contributor.referee3.fl_str_mv Cardoso, Wesley Bueno
dc.contributor.authorLattes.fl_str_mv http://lattes.cnpq.br/6736689883670342
dc.contributor.author.fl_str_mv Bidinotto, Alexandre Borges
contributor_str_mv Avelar, Ardiley Torres
Taillebois, Emile Raymond Ferreira
Avelar, Ardiley Torres
Santana, Ademir Eugênio de
Cardoso, Wesley Bueno
dc.subject.por.fl_str_mv Simetria
Teoria de grupos
Relatividade restrita
Tomografia de estados quânticos
topic Simetria
Teoria de grupos
Relatividade restrita
Tomografia de estados quânticos
Symmetry
Group theory
Special relativity
Quantum state tomography
CIENCIAS EXATAS E DA TERRA::FISICA
dc.subject.eng.fl_str_mv Symmetry
Group theory
Special relativity
Quantum state tomography
dc.subject.cnpq.fl_str_mv CIENCIAS EXATAS E DA TERRA::FISICA
description This dissertation begins with a succinct introduction to group theory to enable the understanding of special relativity theory from a symmetrical point of view. From this perspective, the notion of hierarchy of dynamical variables, which is present in relativity, is introduced to quantum mechanical formalism in order to construct the irreducible unitary representations of the Poincaré group for secondary variables. Given this discussion, the questions regarding the existence of a subset of transformations in which the Wigner rotations associated do not depend on the momenta. In sequence, the relativistic Stern-Gerlach observable is presented. This observable also depends on the momenta, so the initial problem on the density matrices for spin remains unsolved. The open question on the Stern-Gerlach observable is what is the minimum number of measurements in order to fully determine a relativistic density matrix. Both questionings on this dissertation can lead to the determination of the quantum state tomography of relativistic particles, which is the further goal of this document.
publishDate 2022
dc.date.accessioned.fl_str_mv 2022-05-04T15:40:15Z
dc.date.available.fl_str_mv 2022-05-04T15:40:15Z
dc.date.issued.fl_str_mv 2022-04-04
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
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dc.identifier.citation.fl_str_mv BIDINOTTO, A. B. Relativistic symmetry in quantum information theory. 2022. 49 f. Dissertação (Mestrado em Física) - Universidade Federal de Goiás, Goiânia, 2022.
dc.identifier.uri.fl_str_mv http://repositorio.bc.ufg.br/tede/handle/tede/12039
identifier_str_mv BIDINOTTO, A. B. Relativistic symmetry in quantum information theory. 2022. 49 f. Dissertação (Mestrado em Física) - Universidade Federal de Goiás, Goiânia, 2022.
url http://repositorio.bc.ufg.br/tede/handle/tede/12039
dc.language.iso.fl_str_mv eng
language eng
dc.relation.program.fl_str_mv 57
dc.relation.confidence.fl_str_mv 500
500
500
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dc.relation.department.fl_str_mv 25
dc.relation.cnpq.fl_str_mv 185
dc.relation.sponsorship.fl_str_mv 0
dc.rights.driver.fl_str_mv Attribution-NonCommercial-NoDerivatives 4.0 International
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution-NonCommercial-NoDerivatives 4.0 International
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Universidade Federal de Goiás
dc.publisher.program.fl_str_mv Programa de Pós-graduação em Fisica (IF)
dc.publisher.initials.fl_str_mv UFG
dc.publisher.country.fl_str_mv Brasil
dc.publisher.department.fl_str_mv Instituto de Física - IF (RG)
publisher.none.fl_str_mv Universidade Federal de Goiás
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFG
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