Quons: A 3D Language for Quantum Information
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 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.
Cite
@article{arxiv.1612.02630,
title = {Quons: A 3D Language for Quantum Information},
author = {Zhengwei Liu and Alex Wozniakowski and Arthur Jaffe},
journal= {arXiv preprint arXiv:1612.02630},
year = {2018}
}