Abstract Quantum Mechanics (joint work with Bob Coecke)

We introduce a categorical axiomatization of (in the first instance: finitary, non-relativistic) Quantum Mechanics with the following main features.

• We expose the underlying structural mathematics — or logic in a suitably broad sense (very different to traditional quantum logic) — of both quantum and classical information flow, allowing effective reasoning about entanglement in compound systems, and information protocols and computation schemes based on this.
• We develop AQM as a typed theory: the types correspond to important conceptual distinctions in the physical theory. This allows e.g. a proper compositional treatment of measurements.
• The theory is ‘structural’ and ‘qualitative’, yet quantitative features (scalars, a Born rule) arise from it automatically.
• Notions such as projectors, which are fundamental building blocks in the usual formalism, are decomposed in AQM. This decomposition plays a key role in the analysis of quantum information flow.
• There is an attractive graphical calculus which allows the formalism to be presented in an intuitive visual form.

We will illustrate this by deriving the quantum teleportation protocol.

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Last updated by tbourke at Mon Sep 19 15:05:54 2005 GMT+1000