  Within the unified framework of exploiting the relative entropy as a distance
measure of quantum correlations, we make explicit the hierarchical structure of
quantum coherence, quantum discord and quantum entanglement in multipartite
systems. On this basis, we introduce a new measure of quantum coherence, the
basis-free quantum coherence and prove that this quantity is exactly equivalent
to quantum discord. Furthermore, since the original relative entropy of
coherence is a basis-dependent quantity, we investigate the local and nonlocal
unitary creation of quantum coherence, focusing on the two-qubit unitary gates.
Intriguingly, our results demonstrate that nonlocal unitary gates do not
necessarily outperform the local unitary gates. Finally, the additivity
relationship of quantum coherence in tripartite systems is discussed in detail,
where the strong subadditivity of von Neumann entropy plays an essential role.
