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Leonardo Teixeira Neveshttp://lattes.cnpq.br/0525343899407081Reinaldo Oliveira ViannaSebastião José Nascimento de PáduaRaphael Campos DrumondMiguel Angel Solis ProsserDardo Miguel Goyenechehttp://lattes.cnpq.br/5519819239890232Mário Foganholi Fernandes2023-05-29T17:47:18Z2023-05-29T17:47:18Z2022-02-18http://hdl.handle.net/1843/54102We have proposed a new method for quantum state reconstruction, called quantum ptychography. This method is based on an analogy with ptychography, a method for phase retrieval in classical optics. The main advantage of quantum ptychography, when compared to other methods for quantum state reconstruction, is its experimental simplicity: it uses measurements in a single basis, while using intermediate projectors to achieve data diversity; on the other hand, usual methods require measurements in several different bases. By not using many bases, quantum ptychography allows simpler experimental setups. This greater simplicity might be especially invaluable in a context of material scarcity, such as brazilian science has been facing in the recent years. Quantum ptychography is also flexible regarding the intermediate projectors, which allows for the experimenter to customize it to their needs. We have studied the method extensively in the context of pure state reconstruction. We have shown its equivalence to an alternating gradient search, allowing a mathematical understanding of how the method works. We have made numerical simulations of its reconstructions, using realistic amounts of noise, and showed that its reconstructions are excellent. We have also made an experiment with slit qudits to test its performance, and again attained very satisfactory results. As it was with classical ptychography, there are many improvements that quantum ptychography could see. We have also generalized it for mixed states and obtained encouraging preliminary results. With this and other advances, we hope that quantum ptychography can become a useful tool for quantum information.Nós propusemos um novo método para reconstruir estados quânticos, chamado pticografia quântica. Esse método se baseia em uma analogia com a pticografia, um método de reconstrução de fase na óptica clássica. A principal vantagem da pticografia quântica, quando comparada a outros métodos de reconstrução de estado, é sua simplicidade experimental: ela usa medidas em uma única base, ao passo que projetores intermediários são usados para se conseguir a diversidade de dados necessária; por outro lado, os métodos usuais requerem medidas em diversas bases diferentes. Ao não usar diversas bases, a pticografia quântica permite que as montagens experimentais sejam mais simples. Essa maior simplicidade pode ser especialmente valiosa no contexto de escassez material, tal qual a ciência brasileira vem enfrentando nos últimos anos. A pticografia quântica também é flexı́vel com respeito aos projetores intermediários, o que permite ao experimentador ajustá-la às suas necessidades. Nós estudamos esse método a fundo no contexto da reconstrução de estados puros. Nós mostramos a sua equivalência a uma busca por gradientes alternados, o que permite um entendimento matemático do seu funcionamento. Fizemos simulações numéricas de suas reconstruções, usando nı́veis realistas de ruı́do, e mostramos que suas reconstruções são excelentes. Também fizemos um experimento com qudits de fenda para averiguar a sua performance, e novamente obtivemos resultados muito satisfatórios. Assim como a pticografia clássica, a pticografia quântica é passı́vel de diversos avanços. Nós também a generalizamos para estados mistos e obtivemos resultados prelimi- nares encorajadores. Com esse e outros desenvolvimentos, nós esperamos que a pticografia quântica possa se tornar uma ferramenta útil na informação quântica.CNPq - Conselho Nacional de Desenvolvimento Científico e TecnológicoengUniversidade Federal de Minas GeraisPrograma de Pós-Graduação em FísicaUFMGBrasilICX - DEPARTAMENTO DE FÍSICAhttp://creativecommons.org/licenses/by/3.0/pt/info:eu-repo/semantics/openAccessÓpticaMecânica quânticaQuantum state reconstructionPtychographyPhase retrievalQuantum ptychographyPticografia quânticainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisreponame:Repositório Institucional da UFMGinstname:Universidade Federal de Minas Gerais (UFMG)instacron:UFMGLICENSElicense.txtlicense.txttext/plain; charset=utf-82118https://repositorio.ufmg.br/bitstream/1843/54102/5/license.txtcda590c95a0b51b4d15f60c9642ca272MD55ORIGINALTese_QuantumPtychography_pdfa.pdfTese_QuantumPtychography_pdfa.pdfTese em arquivo PDF/A.application/pdf7955860https://repositorio.ufmg.br/bitstream/1843/54102/4/Tese_QuantumPtychography_pdfa.pdf5548c31879401785b6f5155dc0452982MD54CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8914https://repositorio.ufmg.br/bitstream/1843/54102/2/license_rdff9944a358a0c32770bd9bed185bb5395MD521843/541022023-05-29 14:47:18.763oai:repositorio.ufmg.br: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ório InstitucionalPUBhttps://repositorio.ufmg.br/oaiopendoar:2023-05-29T17:47:18Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)false
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