General Probabilistic Theories — From Foundations of Classical and Quantum Theory to Applications in Quantum Information Theory

General probabilistic theories (GPTs) are a mathematical framework that extends both classical and quantum theories, based on fundamental axioms regarding operations on physical systems. GPTs have been actively studied in the context of quantum foundations and the mathematics of quantum information, with the main goal of operationally characterizing mathematical models of classical and quantum theories. In addition, recent efforts have been directed toward applications in quantum information theory. In the first half of this talk, I will briefly introduce the overview and key results of GPTs, explaining the mathematical framework through concrete models. I will then briefly present my recent research on "characterization of physical quantities and non-classicality through intersubjectivity" and "quantitative connections between general probabilistic theories and quantum theory."