  Description of nonclassicality of states has hitherto been through violation
of Bell inequality and non-separability, with the latter being a stronger
constraint. In this paper, we show that this can be further sharpened, by
introducing the concept of classical simulation. A state admits classical
simulation if it can be mimicked fully by a separable state of higher
dimension. A nonclassical state, which we call exceptional, does not admit
classical simulation. Focusing on two qubit states, we show that exceptionality
is more stringent than violation of Bell inequality, and involves an intricate
interplay of coherence and entanglement. The new criterion is shown to provide
a natural description of entangled states which respect Bell inequality, and
also a way of enumerating the classical resources that are required to simulate
a quantum state. Possible implications to quantum dynamics and quantum
information are briefly touched upon.
