Universality of State-Independent Violation of Correlation Inequalities for Noncontextual Theories

We show that the state-independent violation of inequalities for noncontextual hidden variable theories introduced in [Phys. Rev. Lett. 101, 210401 (2008)] is universal, i.e., occurs for any quantum mechanical system in which noncontextuality is meaningful. We describe a method to obtain state-independent violations for any system of dimension $d\ge 3$. This universality proves that, according to quantum mechanics, there are no “classical” states.