Violation of all two-party facet Bell inequalities by almost-quantum correlations

The characterization of the set quantum correlations is a problem fundamental importance in information. question whether every proper (tight) Bell inequality violated Quantum theory an intriguing one this regard. Here, we make significant progress answering question, by showing that tight 'Almost Quantum' correlations, semi-definite programming relaxation correlations. As consequence, show many (classes of) inequalities including two-party correlation and multi-outcome non-local computation games, do not admit violations, are facets classical polytope. To this, use connections between graph-theoretic Lov\'{a}sz-theta set, discovered Cabello-Severini-Winter (CSW). We also exploit cut polytope graph polytope, to define lower dimensional theory. methods enable us derive novel (almost) inequalities, which may be independent interest for self-testing applications.