Quantum reasoning, diagrammatically, automatically
Abstract
We provide both a diagrammatic and logical system to reason about
quantum phenomena. Essential features are entanglement, the flow of
information from the quantum systems into the classical measurement
contexts, and back---these flows are crucial for several quantum informatic
scheme's such as quantum teleportation---, and mutually unbiassed
observables---e.g. position and momentum. The formal structures we use are
kin to those of topological quantum field theories---e.g. monoidal
categories, compact closure, Frobenius objects, coalgebras. We show that
our diagrammatic/logical language is universal. Informal
appetisers can be found in:
* Introducing Categories to the Practicing Physicist
http://web.comlab.ox.ac.uk/oucl/work/bob.coecke/Cats.pdf
* Kindergarten Quantum Mechanics