Quantum independence and chromatic numbers
Combinatorics
2024-02-09 v2 Quantum Physics
Abstract
We construct a new graph on 120 vertices whose quantum and classical independence numbers are different. At the same time, we construct an infinite family of graphs whose quantum chromatic numbers are smaller than the classical chromatic numbers. Furthermore, we discover the relation to Kochen-Specker sets that characterizes quantum cocliques that are strictly bigger than classical ones. Finally, we prove that for graphs with independence number is two, quantum and classical independence numbers coincide.
Cite
@article{arxiv.2401.16518,
title = {Quantum independence and chromatic numbers},
author = {Chris Godsil and Mariia Sobchuk},
journal= {arXiv preprint arXiv:2401.16518},
year = {2024}
}