Generalised Compositional Theories and Diagrammatic Reasoning

TL;DR

This paper introduces diagrammatic calculus as a foundational and mathematical tool for quantum information and foundations, illustrating its use in studying complementarity and non-locality.

Contribution

It presents a unified diagrammatic framework with physical and mathematical foundations applicable to diverse quantum theories.

Findings

Diagrammatic calculus effectively models quantum concepts.

It provides a conceptual backbone for physical theories.

The framework relates to standard mathematical structures.

Abstract

This chapter provides an introduction to the use of diagrammatic language, or perhaps more accurately, diagrammatic calculus, in quantum information and quantum foundations. We illustrate the use of diagrammatic calculus in one particular case, namely the study of complementarity and non-locality, two fundamental concepts of quantum theory whose relationship we explore in later part of this chapter. The diagrammatic calculus that we are concerned with here is not merely an illustrative tool, but it has both (i) a conceptual physical backbone, which allows it to act as a foundation for diverse physical theories, and (ii) a genuine mathematical underpinning, permitting one to relate it to standard mathematical structures.