Classical simulation of entangled states

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.