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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> or =3. This universality proves that, according to quantum mechanics, there are no "classical" states.
Badziąg et al. (Tue,) studied this question.