Through comparisons with an entanglement breaking (EB) channel,we characterize the local quantum channels that destroy quantum correlations,especially for quantum discord,and give a detailed description of a discordbreaking (DB) channel.We prove that the quantum discord can be broken if and only if the local quantum channel is a commutativity-creating (CoC) channel.Then we show which kind of channels is a CoC channel,and address the relation between EB and DB channels.Furthermore we apply our results to three typical noise channels.