  This work is about diagrammatic languages, how they can be represented, and
what they in turn can be used to represent. More specifically, it focuses on
representations and applications of string diagrams. String diagrams are used
to represent a collection of processes, depicted as "boxes" with multiple
(typed) inputs and outputs, depicted as "wires". If we allow plugging input and
output wires together, we can intuitively represent complex compositions of
processes, formalised as morphisms in a monoidal category.
  [...] The first major contribution of this dissertation is the introduction
of a discretised version of a string diagram called a string graph. String
graphs form a partial adhesive category, so they can be manipulated using
double-pushout graph rewriting. Furthermore, we show how string graphs modulo a
rewrite system can be used to construct free symmetric traced and compact
closed categories on a monoidal signature.
  The second contribution is in the application of graphical languages to
quantum information theory. We use a mixture of diagrammatic and algebraic
techniques to prove a new classification result for strongly complementary
observables. [...] We also introduce a graphical language for multipartite
entanglement and illustrate a simple graphical axiom that distinguishes the two
maximally-entangled tripartite qubit states: GHZ and W. [...]
  The third contribution is a description of two software tools developed in
part by the author to implement much of the theoretical content described here.
The first tool is Quantomatic, a desktop application for building string graphs
and graphical theories, as well as performing automated graph rewriting
visually. The second is QuantoCoSy, which performs fully automated,
model-driven theory creation using a procedure called conjecture synthesis.

Category Theory;Artificial Intelligence;Quantum Physics