Quantum theory: finite and infinite dimension study

• Grant number: 17/00697-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: May 01, 2017
• End date: April 30, 2018
• Field of knowledge: Physical Sciences and Mathematics - Physics
• Principal Investigator: Marcelo de Oliveira Terra Cunha
• Grantee: Tales Rick Perche
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

This Project's intention is to conduct a study about the differences between finite and infinite dimensional quantum theory, with proper mathematical accuracy. Therefore it will be necessary for the student to understand Hilbert space algebra, specifically in infinite dimension, and part of the project is reserved for the student to learn Measure Theory and Functional Analysis, intending to formalize infinite dimensional quantum theory. The next step of the project is for comprehending contextuality in quantum theory, for which we will use as reference recent articles that introduce various related themes, mainly Bell Inequalities and Graph Approach. After appropriate formation on the above topics, the project has the objective to relate both, studying contextuality or non-locality scenarios where finite dimension hypothesis may restrict quantum quotas. In particular, it's the project's intention that the I3322 inequality and it's relation to Tsirelson's Problem are understood. (AU)