Quantum ptychography

• Ano de defesa: 2022
• Autor(a) principal: Mário Foganholi Fernandes
• Orientador(a): Leonardo Teixeira Neves
• Banca de defesa: Sebastião José Nascimento de Pádua, Raphael Campos Drumond, Miguel Angel Solis Prosser, Dardo Miguel Goyeneche
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Universidade Federal de Minas Gerais
• Programa de Pós-Graduação: Programa de Pós-Graduação em Física
• Departamento: ICX - DEPARTAMENTO DE FÍSICA
• País: Brasil
• Palavras-chave em Português: Quantum state reconstruction; Ptychography; Phase retrieval
• Link de acesso: http://hdl.handle.net/1843/54102

We 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.