Inverting non-bijective maps through recovering channels
Autor(a) principal: | |
---|---|
Data de Publicação: | 2021 |
Tipo de documento: | Dissertação |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFPE |
Texto Completo: | https://repositorio.ufpe.br/handle/123456789/40219 |
Resumo: | In this dissertation we are interested in the dynamics of open quantum systems in the context of quantum information. First, we investigate the dynamics of one qubit at the regime where an inverse evolution is not well defined. This limit is widely used and explored in this work, called as the limit of non-bijectivity. We demonstrate how to compute a completely positive inverse evolution, based on the theory of recovery maps, here to be the Petz recovery map. The analyzed evolutions are the typical decoherence processes: dephasing, depolarizing and amplitude damping channels in the regime of non-bijectivity. To measure how efficient the Petz can be recovering a random quantum state, we use the fidelity function as the figure of merit. Also, we quantify how non-invertible a dynamics is compared to another. As an application for this formalism, in the second part of this work we show how we can explore recovery maps in the context of non-Markovian evolutions, in order to minimize memory effects. We demonstrate that recovering maps can be useful under certain constraints to simulate a non-Markovian evolution by an “almost” Markovian one. We demonstrate that there exists a strong dependence between the success of this strategy and the initial correlations between system and environment. |
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LAUTENBACHER, Lea Luise Madureirahttp://lattes.cnpq.br/1008468575628682http://lattes.cnpq.br/6588189278676621http://lattes.cnpq.br/8059508629232656BERNARDES, Nadja KolbPARISIO, Fernando Roberto de Luna2021-05-28T22:53:54Z2021-05-28T22:53:54Z2021-03-29LAUTENBACHER, Lea Luise Madureira. Inverting non-bijective maps through recovering channels. 2021. Dissertação (Mestrado em Física) - Universidade Federal de Pernambuco, Recife, 2021.https://repositorio.ufpe.br/handle/123456789/40219In this dissertation we are interested in the dynamics of open quantum systems in the context of quantum information. First, we investigate the dynamics of one qubit at the regime where an inverse evolution is not well defined. This limit is widely used and explored in this work, called as the limit of non-bijectivity. We demonstrate how to compute a completely positive inverse evolution, based on the theory of recovery maps, here to be the Petz recovery map. The analyzed evolutions are the typical decoherence processes: dephasing, depolarizing and amplitude damping channels in the regime of non-bijectivity. To measure how efficient the Petz can be recovering a random quantum state, we use the fidelity function as the figure of merit. Also, we quantify how non-invertible a dynamics is compared to another. As an application for this formalism, in the second part of this work we show how we can explore recovery maps in the context of non-Markovian evolutions, in order to minimize memory effects. We demonstrate that recovering maps can be useful under certain constraints to simulate a non-Markovian evolution by an “almost” Markovian one. We demonstrate that there exists a strong dependence between the success of this strategy and the initial correlations between system and environment.CNPqNesta dissertação estamos interessados na dinâmica de sistemas quânticos abertos no contexto de informação quântica. A princípio, investigamos a dinâmica de um qubit no regime em que uma evolução inversa não está bem definida. Este limite é amplamente explorado neste trabalho, chamado de limite de não-bijetividade. Demonstramos como construir uma evolução inversa que seja um processo físico bem definido, baseado na teoria de mapas de recuperação, aqui o mapa de recuperação Petz. As evoluções analisadas são típicos processos de decoerência: dephasing, depolarizing e amplitude damping, no regime de não-bijetividade. A fim de medir o quão eficiente o Petz recupera um estado quântico aleatório, nós usamos como figura de mérito a função fidelidade. Também, quantificamos o quão não-inversível uma dinâmica é comparada a outra. Como uma aplicação doesse formalismo, na segunda parte do trabalho, mostramos como os mapas de recuperação podem ser explorados em se tratando de evoluções não-Markovianas, a fim de minimizar efeitos de memória. Demonstramos que sob certas circunstâncias os mapas de recuperação podem ser úteis para simular uma evolução não-Markoviana por uma “quase” Markoviana. Evidenciamos que existe uma forte dependência entre o sucesso da estratégia aqui proposta e as correlações iniciais entre sistema e ambienteengUniversidade Federal de PernambucoPrograma de Pos Graduacao em FisicaUFPEBrasilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessFísica Teórica e ComputacionalCanais quânticosMapa de recuperação PetzGrau de não-invertibilidadeInverting non-bijective maps through recovering channelsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesismestradoreponame:Repositório Institucional da UFPEinstname:Universidade Federal de Pernambuco (UFPE)instacron:UFPEORIGINALDISSERTAÇÃO Lea Luise Madureira Lautenbacher.pdfDISSERTAÇÃO Lea Luise Madureira Lautenbacher.pdfapplication/pdf2646333https://repositorio.ufpe.br/bitstream/123456789/40219/1/DISSERTA%c3%87%c3%83O%20Lea%20Luise%20Madureira%20Lautenbacher.pdf01d38acfb81a9e62dcfe1153ef0a4620MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8811https://repositorio.ufpe.br/bitstream/123456789/40219/2/license_rdfe39d27027a6cc9cb039ad269a5db8e34MD52LICENSElicense.txtlicense.txttext/plain; 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dc.title.pt_BR.fl_str_mv |
Inverting non-bijective maps through recovering channels |
title |
Inverting non-bijective maps through recovering channels |
spellingShingle |
Inverting non-bijective maps through recovering channels LAUTENBACHER, Lea Luise Madureira Física Teórica e Computacional Canais quânticos Mapa de recuperação Petz Grau de não-invertibilidade |
title_short |
Inverting non-bijective maps through recovering channels |
title_full |
Inverting non-bijective maps through recovering channels |
title_fullStr |
Inverting non-bijective maps through recovering channels |
title_full_unstemmed |
Inverting non-bijective maps through recovering channels |
title_sort |
Inverting non-bijective maps through recovering channels |
author |
LAUTENBACHER, Lea Luise Madureira |
author_facet |
LAUTENBACHER, Lea Luise Madureira |
author_role |
author |
dc.contributor.authorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/1008468575628682 |
dc.contributor.advisorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/6588189278676621 |
dc.contributor.advisor-coLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/8059508629232656 |
dc.contributor.author.fl_str_mv |
LAUTENBACHER, Lea Luise Madureira |
dc.contributor.advisor1.fl_str_mv |
BERNARDES, Nadja Kolb |
dc.contributor.advisor-co1.fl_str_mv |
PARISIO, Fernando Roberto de Luna |
contributor_str_mv |
BERNARDES, Nadja Kolb PARISIO, Fernando Roberto de Luna |
dc.subject.por.fl_str_mv |
Física Teórica e Computacional Canais quânticos Mapa de recuperação Petz Grau de não-invertibilidade |
topic |
Física Teórica e Computacional Canais quânticos Mapa de recuperação Petz Grau de não-invertibilidade |
description |
In this dissertation we are interested in the dynamics of open quantum systems in the context of quantum information. First, we investigate the dynamics of one qubit at the regime where an inverse evolution is not well defined. This limit is widely used and explored in this work, called as the limit of non-bijectivity. We demonstrate how to compute a completely positive inverse evolution, based on the theory of recovery maps, here to be the Petz recovery map. The analyzed evolutions are the typical decoherence processes: dephasing, depolarizing and amplitude damping channels in the regime of non-bijectivity. To measure how efficient the Petz can be recovering a random quantum state, we use the fidelity function as the figure of merit. Also, we quantify how non-invertible a dynamics is compared to another. As an application for this formalism, in the second part of this work we show how we can explore recovery maps in the context of non-Markovian evolutions, in order to minimize memory effects. We demonstrate that recovering maps can be useful under certain constraints to simulate a non-Markovian evolution by an “almost” Markovian one. We demonstrate that there exists a strong dependence between the success of this strategy and the initial correlations between system and environment. |
publishDate |
2021 |
dc.date.accessioned.fl_str_mv |
2021-05-28T22:53:54Z |
dc.date.available.fl_str_mv |
2021-05-28T22:53:54Z |
dc.date.issued.fl_str_mv |
2021-03-29 |
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.citation.fl_str_mv |
LAUTENBACHER, Lea Luise Madureira. Inverting non-bijective maps through recovering channels. 2021. Dissertação (Mestrado em Física) - Universidade Federal de Pernambuco, Recife, 2021. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufpe.br/handle/123456789/40219 |
identifier_str_mv |
LAUTENBACHER, Lea Luise Madureira. Inverting non-bijective maps through recovering channels. 2021. Dissertação (Mestrado em Física) - Universidade Federal de Pernambuco, Recife, 2021. |
url |
https://repositorio.ufpe.br/handle/123456789/40219 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
http://creativecommons.org/licenses/by-nc-nd/3.0/br/ info:eu-repo/semantics/openAccess |
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http://creativecommons.org/licenses/by-nc-nd/3.0/br/ |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de Pernambuco |
dc.publisher.program.fl_str_mv |
Programa de Pos Graduacao em Fisica |
dc.publisher.initials.fl_str_mv |
UFPE |
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Brasil |
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Universidade Federal de Pernambuco |
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Repositório Institucional da UFPE |
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