Statistical Robustness of Experimental Implementations of Non-locality and Contextuality in the n-cycle scenarios

• Grant number: 22/14069-1
• Support Opportunities: Scholarships abroad - Research Internship - Master's degree
• Start date: February 27, 2023
• End date: August 26, 2023
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Bárbara Lopes Amaral
• Grantee: Gustavo Balvedi Pimentel
• Supervisor: Antonio Acin
• Host Institution: Instituto de Física (IF). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: Institut de Ciencies Fotoniques (ICFO), Spain
• Associated to the scholarship: 22/01421-9 - Symmetries of non-contextuality inequalities and the statistical robustness of experimental implementations, BP.MS

Abstract

In an ideal contextuality scenario, it is assumed that whenever two contexts overlap, the marginal distribution obtained for the intersection of these contexts must be the same. Although this nondisturbance idealization has been extremely useful in investigating the limitations of physical theories, it is necessary to develop a more robust and experimentally-friendly framework for contextuality. In this project we will investigate one of these alternatives and look for generalizations of the proposal of reference J. Phys. A: Math. Theor. 50 255301 (2017). Our main goal is to consider different versions of nonlocality and noncontextuality inequalities using group symmetries. Different variants of aBell inequality are known to be equivalent when evaluated on nonsignaling behaviors. However, in experimental setups, the robustness of the violation depends on the chosen inequality variant. In reference J. Phys. A: Math. Theor. 50 255301 (2017), the authors explain that phenomenonusing the decomposition of the space of outcome probability distributions under the action of the symmetry group of the scenario, and propose a method to optimize the statistical robustness of a Bell inequality. We conjecture that similar ideas hold for general contextuality scenarios and we want to investigate when such optimizationcan be applied in a special class of scenarios, called the 5[-cycle scenarios.