Numerical Determination of Local Models in Networks

• Autor(a) principal: SILVA FILHO, José Mário da
• Data de Publicação: 2022
• Tipo de documento: Dissertação
• Idioma: eng
• Título da fonte: Repositório Institucional da UFPE
• dARK ID: ark:/64986/00130000048wx
• Texto Completo: https://repositorio.ufpe.br/handle/123456789/45707
• topic: Física teórica e computacional; Não-localidade quântica em redes; Modelos n-locais; Não-localidade de Bell

Taking advantage of the fact that the cardinalities of hidden variables in network scenarios can be taken to be finite without loss of generality, a numerical tool for finding explicit local models that reproduce a given statistical behaviour was developed. The numerical procedure was then applied to get numerical estimates to two interesting problems in the context of network non-locality: i) for which critical visibility the Greenberger-Horne-Zeilinger (GHZ) distribution ceases to be local in the triangle scenario with no inputs; ii) what is the boundary of the local set in a given 2-dimensional slice of the probability space for the bilocal network with binary inputs and outputs. For the first problem: a critical visibility of v ≈ 1/3 was found; behaviours with v ≤ 1/3 were proven to be trilocal; and numerical evidence that behaviours with v > 1/3 are not trilocal was found. For the second problem: a closed set that approximates the bilocal set was found; behaviours inside this set were proven to be bilocal; and numerical evidence that behaviours outside this set are not bilocal was found.