Holographic Software for Quantum Networks

TL;DR

This paper presents holographic software that visually represents quantum networks, enabling topological simulation and new multipartite communication protocols, bridging planar para algebras and quantum information.

Contribution

It introduces a novel pictorial approach to quantum information that connects topological and algebraic methods, including the string Fourier transform and new communication protocols.

Findings

Pictorial software captures algebraic and topological quantum network aspects

Topological simulation of quantum networks using holographic software

Discovery of new multipartite communication protocols

Abstract

We introduce a pictorial approach to quantum information, called holographic software. Our software captures both algebraic and topological aspects of quantum networks. It yields a bi-directional dictionary to translate between a topological approach and an algebraic approach. Using our software, we give a topological simulation for quantum networks. The string Fourier transform (SFT) is our basic tool to transform product states into states with maximal entanglement entropy. We obtain a pictorial interpretation of Fourier transformation, of measurements, and of local transformations, including the $n$-qudit Pauli matrices and their representation by Jordan-Wigner transformations. We use our software to discover interesting new protocols for multipartite communication. In summary, we build a bridge linking the theory of planar para algebras with quantum information.