  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 > 2. This
universality proves that, according to quantum mechanics, there are no
"classical" states.
