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

Pictures of Processes: Automated Graph Rewriting for Monoidal Categories and Applications to Quantum Computing