Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model

A state of a composite quantum system is called classically correlated if it can be approximated by convex combinations of product states, and Einstein-Podolsky-Rosen correlated otherwise. Any classically correlated state can be modeled by a hidden-variable theory and hence satisfies all generalized Bell’s inequalities. It is shown by an explicit example that the converse of this statement is false.