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

• Grant number: 22/01421-9
• Support Opportunities: Scholarships in Brazil - Master
• Start date: April 01, 2022
• End date: September 30, 2024
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Bárbara Lopes Amaral
• Grantee: Gustavo Balvedi Pimentel
• Host Institution: Instituto de Física (IF). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 20/06454-7 - Non-locality and contextuality as resources for quantum information, quantum computation and the certification of quantum devices, AP.JP
• Associated scholarship(s): 22/14069-1 - Statistical Robustness of Experimental Implementations of Non-locality and Contextuality in the n-cycle scenarios, BE.EP.MS

Abstract

Quantum non-locality and contextuality are a consequence of the impossibility of explaining the probabilities of measurement results in quantum systems from pre-existing values that are independent of other compatible measurements that can be jointly performed. Non-locality and contextuality are two surprising characteristics of quantum theory and we believe that understanding them is a key step to explain quantum physics from first principles, one of the greatest challenges of recent times. Besides the evident importance of non-locality and contextuality for foundations of quantum theory, they have also been identified as resources for quantum computation, in addition to other applications. Experimental verification of contextuality has attracted much attention over the past years, and we expect that the recognition of contextuality as an operational resource for quantum information will increase this interest. It is thus of utmost importance to develop a robust theoretical framework for contextuality that can be efficiently applied to real experiments. In particular, it is important to design a sound theoretical machinery well-adapted to cases in which the sets of measurements do not satisfy the assumption of non-disturbance, which is an strong restriction that will hardly be perfectly satisfied in real experiments. It is crucial to investigate alternative frameworks for non-locality and contextuality from an operational perspective, and develop an experimentally-friendly theoretical framework for the treatment of contextuality as a resource. In this project we will investigate one of these alternatives and look for generalizationsof the proposal made by Renou et. al. Our main goal is to consider different versions of Bell and non-contextuality inequalities using group symmetries. Different variants of a Bell inequality are known to be equivalent when evaluated on non-signaling behaviors. However, in experimental setups, the robustness of the violation depends on the chosen inequality variant. Renou et. al. explain this phenomenon using 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 optimization can be applied. This problem will be investigated in partnership with Dr. Denis Rosset from Perimeter Institute.