  We propose a 2-categorical formalism for describing classical information,
quantum systems, and their interactions, based on the principle that classical
information can be encoded as correlations between quantum systems. Applying
this in the 2-category of 2-Hilbert spaces recovers ordinary quantum theory.
The formalism gives a simple, graphical way to describe the specification and
implementation of certain quantum procedures, which we use to investigate
quantum teleportation, dense coding, complementarity and quantum erasure,
verifying our results computationally using a software package.
