Higher Quantum Theory

TL;DR

This paper introduces a 2-categorical framework for quantum theory that encodes classical information as correlations between quantum systems, providing a graphical language for quantum procedures and verifying key quantum phenomena.

Contribution

It develops a novel 2-categorical formalism for quantum theory that unifies classical and quantum information, enabling new graphical descriptions of quantum protocols.

Findings

Recovering ordinary quantum theory within the 2-Hilbert space framework

Graphical descriptions of quantum teleportation, dense coding, and complementarity

Computational verification of quantum procedures using software

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.