Symmetries of non-contextuality inequalities and the statistical robustness of experimental implementations

• Ano de defesa: 2025
• Autor(a) principal: Pimentel, Gustavo Balvedi
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Bell Inequalities; Contextualidade Quântica; Desigualdades de Bell; Group Representation Theory; Não-localidade Quântica; Quantum Contextuality; Quantum Non-locality; Teoria de Representações de Grupos.
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/43/43134/tde-12032025-171526/

Quantum non-locality and quantum contextuality result from the impossibility of explain- ing the probabilities of measurement outcomes in quantum systems using theoretical mod- els that assume that observables have well-defined values prior to the measurement, and that these values do not depend on which other compatible measurements are performed simultaneously to the measurement. These two features are not only of foundational im- portance for quantum theory, but are also recognized as resources for quantum computing and other applications. The experimental verification of contextuality has garnered significant attention, and its recognition as an operational resource for quantum information is expected to further fuel this interest. Developing a robust theoretical framework for contextuality that is both operationally grounded and experimentally applicable is crucial. Particularly, real-world experiments often violate the non-disturbance assumption, requiring alternative frame- works that remain effective under such conditions. This dissertation builds upon a recent work by Renou et.al, which explores how dif- ferent variants of a Bell inequality, despite being equivalent under the condition of no- signaling, are not equally robust in real experiments. In order to do so, they propose a method which employs the group of symmetries of a Bell scenario to analyze and op- timize the robustness of Bell inequalities. The primary goal of this dissertation is to generalize this method to contextuality scenarios, exploring the role of group representa- tion theory in optimizing inequalities, and enhancing both theoretical understanding and experimental applicability.