Entanglement is one of the pillars of quantum mechanics and quantum information processing, and as a result, the quantumness of nonentangled states has typically been overlooked and unrecognized until the last decade. We give a robust definition for the classicality versus quantumness of a single multipartite quantum state, a set of states, and a protocol using quantum states. We show a variety of nonentangled (separable) states that exhibit interesting quantum properties, and we explore the "zoo" of separable states; several interesting subclasses are defined based on the diagonalizing bases of the states, and their nonclassical behavior is investigated.The work of BG was funded by EPSRC and Sidney Sussex College, Cambridge. T.M was funded by the Wolfson Foundation and the Israeli MOD Research and Technology Unit. AB and TM were partly supported The Gerald Schwartz & Heather Reis- man Foundation
