Quons: A 3D Language for Quantum Information

TL;DR

This paper introduces a 3D topological language for quantum information, representing quons as composite particles in a 3D manifold, enabling new insights and simplified protocols for quantum operations.

Contribution

It develops a novel 3D topological framework for quantum information, including a new relation and simplified representations of quantum gates and teleportation.

Findings

Topological interpretation of $C^{*}$ Hopf algebra relations

3D representation of CNOT gate

Topological protocol for teleportation

Abstract

We present a 3D, topological picture-language for quantum information. Our approach combines charged excitations carried by strings, with topological properties that arise from embedding the strings in the interior of a three-dimensional manifold with boundary. A quon is a composite that acts as a particle. Specifically a quon is a hemisphere containing a neutral pair of open strings with opposite charge. We interpret multi-quons and their transformations in a natural way. We obtain a new type of relation, a string-genus "joint relation," involving both a string and the 3D manifold. We use the joint relation to obtain a topological interpretation of the $C^{*}$ Hopf algebra relations, that are widely used in tensor networks. We obtain a 3D representation of the Controlled NOT or CNOT gate (that is considerably simpler than earlier work) and a 3D topological protocol for teleportation.