This thesis explores the fundamental aspects of categorical quantum mechanics and its graphical calculus. We introduce the theory of classical-quantum processes to illustrate how information flows between the classical and quantum realms. With these tools in hand, we address several theorems in quantum foundations. Our goal is to express Peres-Mermin’s proof of the Kochen-Specker theorem within a quantumprocess framework, but we encounter challenges that prevent us from fully completing the proof. This negative result suggests a potential incompatibility between categorical quantum mechanics and quantum logic.
