  Quantum discord has been studied extensively as a measure of non-classical
correlations which includes entanglement as a subset. Although it is well known
that non-zero discord can exist without entanglement, the origin of quantum
discord is not well understood as compared to entanglement, which manifests
itself more simply as inseparable higher dimensional quantum superposition. In
this paper we establish the discordlike correlation of bipartite coherence and
then compare it to quantum discord. Consequently, we show that the minimum of
the discordlike correlation of coherence coincides with the original quantum
discord. This demonstrates quantum discord as the irreducible correlated
bipartite coherence. In addition, the discordlike correlated coherence is shown
to admit the postulates of the quantum resource theory (QRT), although the
original quantum discord is not a "good" candidate under the QRT. We also find
that the relative entropy measure induced from the discordlike coherence is a
well-defined coherence measure for bipartite states.
