On quantum symmetries of graphs

TL;DR

This paper investigates quantum automorphisms of finite graphs, demonstrating that for graphs with at least three vertices, the associated quantum graphs exhibit nonlocal symmetries and perfect quantum no-signaling correlations.

Contribution

It introduces the study of quantum automorphism groups of quantum graphs derived from finite graphs and proves the existence of nonlocal symmetries for graphs with three or more vertices.

Findings

Quantum graphs associated with graphs of size ≥ 3 admit nonlocal symmetry.

Existence of perfect quantum no-signaling correlations in these quantum graphs.

Analysis of the game algebra of quantum automorphisms of quantum graphs.

Abstract

Let $G$ be a simple finite graph, and let $\mathcal U_G$ be the related quantum graph. We study the game algebra $C(\mathrm{Qut}(\mathcal U_G))$ of quantum automorphism of $\mathcal U_G$. Moreover, we prove that for any graph $G$ with $|V(G)|\geq 3$, the quantum graph $\mathcal U_G$ admits nonlocal symmetry, meaning that there exists a perfect quantum no-signaling correlation