Generalised process theories
Categorical quantum mechanics uses the mathematical framework of monoidal categories to provide a concise, elegant axiomatisation of quantum theory. This provides a powerful and intuitive graphical calculus to describe quantum processes such as teleportation, algorithms and cryptography in a much simpler way.
Another benefit of the categorical approach is that it sets up quantum theory in a more general framework of theories known as process theories. This provides a new viewpoint of quantum theory, which puts composition of systems at its heart, avoiding many problems that have plagued other approaches to quantum theory such as quantum logic.
Other theories that are of interest in quantum foundations also fit into this framework. For example Spekkens toy model has been formalised in terms of category theory providing new insights into (non)locality in quantum theory. In my work I have considered another toy theory, modal quantum theory, finding that it has a simplified description in terms of process theories. This has revealed connections to quantum logic and another framework for toy theories called Chu spaces which I am currently exploring.