In this talk, we discuss how the decomposition result of Koashi-Imoto theorem can be applied to catalysis of correlated quantum randomness. The Koashi-Imoto theorem provides the decomposition of a set of quantum states into which classical and quantum sector and only classical sectors can withstand the action of nontrivial quantum channels. This result provides a useful tool for understanding the structure of bipartite quantum states as one can understand how only classical correlation can be read out while quantum correlation is sensitive to nontrivial quantum channels.