On Quantum Symmetries of Graphs

Journal article, 2026

Let G be a simple finite graph and let UG be the corresponding quantum graph. We study the game algebra C(Qut(UG)) of the quantum automorphisms of UG. It is shown that, for the complete graph Kn, the algebra C(Qut(UKn)) is not commutative even for all n ≥ 3, unlike C(Qut(Kn)) = C(Sn+). Moreover, we prove that, for any graph G with |V (G)| ≥ 3, the quantum graph UG admits nonlocal symmetry, which means that there exists a perfect quantum no-signaling correlation for the quantum automorphism game for UG, which is not local.