Arkhipov’s theorem, graph minors, and linear system nonlocal games

The perfect quantum strategies of a linear system game correspond to certain representations its solution group. We study the groups graph incidence games, which are games in underlying is (non-properly) two-coloured graph. While it undecidable determine whether general has strategy, for this problem solved by Arkhipov’s theorem, states that connected strategy if and only either classical or nonplanar. criterion can be rephrased as forbidden minor condition on graphs. extend theorem showing that, graphs, every quotient closed property group characterization. rederive from theoretic point view, then find minors two new properties: finiteness abelianness. Our methods entirely combinatorial, finding other properties seems an interesting combinatorial problem.