List of papersThis thesis is based on the following papers:1. (Reproduced from [1], with the permission of AIP Publishing) Ryo Takakura, Takayuki Miyadera, "Preparation Uncertainty Implies Measurement Uncertainty in a Class of Generalized Probabilistic Theories", Journal of Mathematical Physics, 61, 082203 (2020); 2. ([2]) Ryo Takakura, Takayuki Miyadera, "Entropic uncertainty relations in a class of generalized probabilistic theories", Journal of Physics A: Mathematical and Theoretical, 54, 315302 (2021); 3. ([3]) Teiko Heinosaari, Takayuki Miyadera, Ryo Takakura, "Testing incompatibility of quantum devices with few states", Physical Review A, 104, 032228 (2021); 4. ([4]) Ryo Takakura, "Entropy of mixing exists only for classical and quantumlike theories among the regular polygon theories",