  Quantum coherence, incompatibility, and quantum correlations are fundamental
features of quantum physics. A unified view of those features is crucial for
revealing quantitatively their intrinsic connections. We define the relative
quantum coherence of two states as the coherence of one state in the reference
basis spanned by the eigenvectors of another one and establish its quantitative
connections with the extent of mutual incompatibility of two states. We also
show that the proposed relative quantum coherence, which can take any form of
measures such as $l_1$ norm and relative entropy, can be interpreted as or
connected to various quantum correlations such as quantum discord, symmetric
discord, entanglement of formation, and quantum deficits. Our results reveal
conceptual implications and basic connections of quantum coherence, mutual
incompatibility, and quantum correlations.
