Relativistic symmetry in quantum information theory

• Ano de defesa: 2022
• Autor(a) principal: Bidinotto, Alexandre Borges
• Orientador(a): Avelar, Ardiley Torres
• 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

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.