A quasiprobability based criterion for classifying the states of N spin-1/2 as classical or non-classical

Based on the concept of joint quasiprobability of the eigenstates of non-commuting components of a spin, a criterion is proposed to characterize the states of a system of N spin-1/2s as classical or nonclassical. That criterion characterizes any state of a spin-1/2 and a factorizable state of N spin-1/2s as classical. It correctly identifies any pure entangled state of two spin-1/2s, an entangled eigenstate of any component of exchange symmetric spin system and squeezed spin states as non-classical.