  Resource theory of quantum coherence originated like entanglement in quantum
information theory. However, still now proper classification of quantum states
is missing under coherence. In this work, we have provided a classification of
states under local incoherent operations. We have succeeded in deriving the
necessary and sufficient condition for which two pure multipartite states are
equivalent under stochastic local incoherent operations and classical
communications (SLICC) and local incoherent operations and classical
communications (LICC). In particular, we have succeeded in characterizing three
qubit pure states under SLICC. Our result reveals the existence of infinite
number of SLICC inequivalent classes for three qubit systems.
