Higher Quantum Theory

Abstract

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.