Foundational Structures and Methods for Quantum Informatics

Quantum Mechanics offers radically new possibilities for information processing, with phenomena such as entanglement --- the possibility of strong instantaneous correlations between spatially separated particles, leading to highly counter-intuitive non-local effects --- playing a central role. Current methods for dealing with these ideas, and with the subtle interplays and information flows between a quantum system and its classical observer, are cumbersome, and somewhat like the early days of programming computers in machine code. In this proposal, building on our previous work, we aim to use ideas and methods which have already proved useful in Computer Science to develop an elegant, conceptual approach, both to the foundations of Quantum Mechanics itself, and to the description, design and analysis of quantum information processing systems. The effect is something like having a high-level programming language --- in which the `computer' is the physical world! While the underlying mathematics we use (category theory) is quite abstract, it is accompanied by a very intuitive diagrammatic formalism, which is useful both as a practical tool for calculations, and for bringing the ideas to life in a very vivid and visual fashion. This formalism also leads to fascinating and unexpected links with logic --- our diagrams can be seen as graphical representations of formal proofs --- and with geometric ideas such as knots and braids.