Discordlike correlation of bipartite coherence

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.