Categorical Quantum Mechanics I: Causal Quantum Processes

Abstract

We derive the category-theoretic backbone of quantum theory from a process ontology. More specifically, we treat quantum theory as a theory of systems, processes and their interactions. In this first part of a three-part overview, we first present a general theory of diagrams, and in particular, of string diagrams. We discuss why diagrams are a very natural starting point for developing scientific theories. Then we define process theories, and define a very general notion of quantum type. We show how our process ontology enables us to assert causality, that is, compatibility of quantum theory and relativity theory, and we prove the no-signalling theorem. Other notable contributions include new, elegant derivations of the no-broadcasting theorem, unitarity of evolution, and Stinespring dilation, all for any 'quantum' type in a general class of process theories.