We present a purely diagrammatic account on quantum theory. The conceptual underpinning is to take composition of systems as the primitive connective, having drawn lessons from some of the shortcomings of other axiomatic approaches. The symbolic underpinning of the approach is category theory, but any reference or prerequisite is avoided by means of the diagrammatic format. Even at an abstract level (i.e. not yet in Hilbert space) a full account can be given on quantum information and quantum foundations. The approach also favours general processes over states, and even sheds a new light on the role of measurement in quantum theory.
Ref: Bob Coecke and Aleks Kissinger (2014, forthcoming) Picturing Quantum Processes. Cambridge University Press.Related work: Some recent other approaches in quantum foundations have meanwhile adopted the diagrammatic paradigm, e.g. Hardy and Chiribella-D’Ariano-Perinotti for an operational foundation, and Coecke-Spekkens for an inferential foundation.