Complementariedade, emaranhamento, incerteza e invariância de Lorentz
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Manancial - Repositório Digital da UFSM |
Texto Completo: | http://repositorio.ufsm.br/handle/1/22159 |
Resumo: | Bohr’s complementarity principle was introduced as a qualitative statement about quantum systems, which have properties that are equally real, but mutually exclusive. This principle, together with the uncertainty principle, is at the origin of Quantum Mechanics (QM), following the development of the theory since then. Another intriguing aspect of QM is entanglement, which is a type of correlation that is only possible within the mathematical formalism of QM. Its central importance in the Quantum foundations, as well as its important role in the fields of quantum information and quantum computation, has made the theory of entanglement achieve great progress in recent decades. In this dissertation we discuss the aspects and relations among complementarity relations, uncertainty, and entanglement. Such aspects are also investigated in relativistic scenarios, since the interest on how entanglement behaves in relativistic scenarios has grown more and more. First, by exploring the properties of the density operator, we obtain complementarity relations, using coherence measures well known in the literature. Next, we show that it is possible to obtain complete complementarity relations, i.e., relations that also take into account entanglement. For this, we explore the purity of a multipartite quantum system. In addition, we discuss the relation between complementarity and uncertainty of an observable, since it is possible to decompose uncertainty into its classical and quantum parts. We also obtain complementarity relations for uncertainty. Finally, we study the complete complementary relations and its Lorentz invariance. Although it is known that entanglement entropy does not remain invariant under Lorentz transformations, and neither does the measures that quantifies complementarity, we show that theses measures when taken together, in a complete complementarity relation, are Lorentz invariant. |
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Complementariedade, emaranhamento, incerteza e invariância de LorentzComplementarity, entanglement, uncertainty and Lorentz invarianceComplementariedadeIncertezaEmaranhamentoInvariância de LorentzComplementarityUncertaintyEntanglementLorentz invarianceCNPQ::CIENCIAS EXATAS E DA TERRA::FISICABohr’s complementarity principle was introduced as a qualitative statement about quantum systems, which have properties that are equally real, but mutually exclusive. This principle, together with the uncertainty principle, is at the origin of Quantum Mechanics (QM), following the development of the theory since then. Another intriguing aspect of QM is entanglement, which is a type of correlation that is only possible within the mathematical formalism of QM. Its central importance in the Quantum foundations, as well as its important role in the fields of quantum information and quantum computation, has made the theory of entanglement achieve great progress in recent decades. In this dissertation we discuss the aspects and relations among complementarity relations, uncertainty, and entanglement. Such aspects are also investigated in relativistic scenarios, since the interest on how entanglement behaves in relativistic scenarios has grown more and more. First, by exploring the properties of the density operator, we obtain complementarity relations, using coherence measures well known in the literature. Next, we show that it is possible to obtain complete complementarity relations, i.e., relations that also take into account entanglement. For this, we explore the purity of a multipartite quantum system. In addition, we discuss the relation between complementarity and uncertainty of an observable, since it is possible to decompose uncertainty into its classical and quantum parts. We also obtain complementarity relations for uncertainty. Finally, we study the complete complementary relations and its Lorentz invariance. Although it is known that entanglement entropy does not remain invariant under Lorentz transformations, and neither does the measures that quantifies complementarity, we show that theses measures when taken together, in a complete complementarity relation, are Lorentz invariant.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESO princípio de complementaridade de Bohr foi introduzido como uma afirmação qualitativa sobre sistemas quânticos únicos, que possuem propriedades que são igualmente reais, mas mutuamente excludentes. Tal princípio, junto com o princípio da incerteza, está na gênese da Mecânica Quântica (MQ), acompanhando o desenvolvimento da teoria desde então. Outro aspecto intrigante da MQ é o emaranhamento, sendo este um tipo de correlação ligada à não separabilidade dentro do formalismo matemático da MQ. Sua importância central nos fundamentos da MQ, bem como seu importante papel nos campos da informação quântica e computação quântica, fez com que a teoria do emaranhamento alcançasse grande progresso nas décadas recentes. Nesta dissertação, nos propomos a discutir relações de complementariedade, incerteza e emaranhamento, bem como abordar tais aspectos em cenários relativísticos, uma vez que o interesse sobre como emaranhamento se comporta em cenários relativísticos tem crescido cada vez mais. Primeiramente, explorando as propriedades do operador densidade, obtemos relações de complementariedade, usando medidas de coerência bem conhecidas na literatura. Em seguida, mostramos que é possível obter relações completas de complementariedade, levando em conta emaranhamento. Para isso, exploramos a pureza de um sistema quântico de muitas partes. Além disso, discutimos a relação entre complementariedade e incerteza de um observável, uma vez que é possível decompor incerteza em suas partes clássica e quântica. Também obtemos relações de complementariedade para incerteza. Por fim, estudamos as relações completas de complementariedade e sua invariância frente a transformações de Lorentz. Embora sabe-se que entropia de emaranhamento não permaneça invariante sob transformações de Lorentz, e tampouco as medidas que quantificam o princípio da complementariedade, quando tomadas juntas, em uma relação de complementaridade completa, são invariantes de Lorentz.Universidade Federal de Santa MariaBrasilFísicaUFSMPrograma de Pós-Graduação em FísicaCentro de Ciências Naturais e ExatasMaziero, Jonashttp://lattes.cnpq.br/1270437648097538Angelo, Renato MoreiraCéleri, Lucas ChibebeBasso, Marcos Leopoldo Wayhs2021-09-08T11:34:00Z2021-09-08T11:34:00Z2021-05-20info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisapplication/pdfhttp://repositorio.ufsm.br/handle/1/22159porAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessreponame:Manancial - Repositório Digital da UFSMinstname:Universidade Federal de Santa Maria (UFSM)instacron:UFSM2021-09-10T06:02:28Zoai:repositorio.ufsm.br:1/22159Biblioteca Digital de Teses e Dissertaçõeshttps://repositorio.ufsm.br/ONGhttps://repositorio.ufsm.br/oai/requestatendimento.sib@ufsm.br||tedebc@gmail.comopendoar:2021-09-10T06:02:28Manancial - Repositório Digital da UFSM - Universidade Federal de Santa Maria (UFSM)false |
dc.title.none.fl_str_mv |
Complementariedade, emaranhamento, incerteza e invariância de Lorentz Complementarity, entanglement, uncertainty and Lorentz invariance |
title |
Complementariedade, emaranhamento, incerteza e invariância de Lorentz |
spellingShingle |
Complementariedade, emaranhamento, incerteza e invariância de Lorentz Basso, Marcos Leopoldo Wayhs Complementariedade Incerteza Emaranhamento Invariância de Lorentz Complementarity Uncertainty Entanglement Lorentz invariance CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA |
title_short |
Complementariedade, emaranhamento, incerteza e invariância de Lorentz |
title_full |
Complementariedade, emaranhamento, incerteza e invariância de Lorentz |
title_fullStr |
Complementariedade, emaranhamento, incerteza e invariância de Lorentz |
title_full_unstemmed |
Complementariedade, emaranhamento, incerteza e invariância de Lorentz |
title_sort |
Complementariedade, emaranhamento, incerteza e invariância de Lorentz |
author |
Basso, Marcos Leopoldo Wayhs |
author_facet |
Basso, Marcos Leopoldo Wayhs |
author_role |
author |
dc.contributor.none.fl_str_mv |
Maziero, Jonas http://lattes.cnpq.br/1270437648097538 Angelo, Renato Moreira Céleri, Lucas Chibebe |
dc.contributor.author.fl_str_mv |
Basso, Marcos Leopoldo Wayhs |
dc.subject.por.fl_str_mv |
Complementariedade Incerteza Emaranhamento Invariância de Lorentz Complementarity Uncertainty Entanglement Lorentz invariance CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA |
topic |
Complementariedade Incerteza Emaranhamento Invariância de Lorentz Complementarity Uncertainty Entanglement Lorentz invariance CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA |
description |
Bohr’s complementarity principle was introduced as a qualitative statement about quantum systems, which have properties that are equally real, but mutually exclusive. This principle, together with the uncertainty principle, is at the origin of Quantum Mechanics (QM), following the development of the theory since then. Another intriguing aspect of QM is entanglement, which is a type of correlation that is only possible within the mathematical formalism of QM. Its central importance in the Quantum foundations, as well as its important role in the fields of quantum information and quantum computation, has made the theory of entanglement achieve great progress in recent decades. In this dissertation we discuss the aspects and relations among complementarity relations, uncertainty, and entanglement. Such aspects are also investigated in relativistic scenarios, since the interest on how entanglement behaves in relativistic scenarios has grown more and more. First, by exploring the properties of the density operator, we obtain complementarity relations, using coherence measures well known in the literature. Next, we show that it is possible to obtain complete complementarity relations, i.e., relations that also take into account entanglement. For this, we explore the purity of a multipartite quantum system. In addition, we discuss the relation between complementarity and uncertainty of an observable, since it is possible to decompose uncertainty into its classical and quantum parts. We also obtain complementarity relations for uncertainty. Finally, we study the complete complementary relations and its Lorentz invariance. Although it is known that entanglement entropy does not remain invariant under Lorentz transformations, and neither does the measures that quantifies complementarity, we show that theses measures when taken together, in a complete complementarity relation, are Lorentz invariant. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-09-08T11:34:00Z 2021-09-08T11:34:00Z 2021-05-20 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://repositorio.ufsm.br/handle/1/22159 |
url |
http://repositorio.ufsm.br/handle/1/22159 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.rights.driver.fl_str_mv |
Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Universidade Federal de Santa Maria Brasil Física UFSM Programa de Pós-Graduação em Física Centro de Ciências Naturais e Exatas |
publisher.none.fl_str_mv |
Universidade Federal de Santa Maria Brasil Física UFSM Programa de Pós-Graduação em Física Centro de Ciências Naturais e Exatas |
dc.source.none.fl_str_mv |
reponame:Manancial - Repositório Digital da UFSM instname:Universidade Federal de Santa Maria (UFSM) instacron:UFSM |
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Universidade Federal de Santa Maria (UFSM) |
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UFSM |
institution |
UFSM |
reponame_str |
Manancial - Repositório Digital da UFSM |
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Manancial - Repositório Digital da UFSM |
repository.name.fl_str_mv |
Manancial - Repositório Digital da UFSM - Universidade Federal de Santa Maria (UFSM) |
repository.mail.fl_str_mv |
atendimento.sib@ufsm.br||tedebc@gmail.com |
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1805922025788669952 |