  Quantum coherence and distributed correlations among subparties are often
considered as separate, although operationally linked to each other, properties
of a quantum state. Here, we propose a measure able to quantify the
contributions derived by both the tensor structure of the multipartite Hilbert
space and the presence of coherence inside each of the subparties. Our results
hold for any number of partitions of the Hilbert space. Within this unified
framework, global coherence of the state is identified as the ingredient
responsible for the presence of distributed quantum correlations, while local
coherence also contributes to the quantumness of the state. A new quantifier,
the "hookup", is introduced within such a framework. We also provide a simple
physical interpretation, in terms of coherence, of the difference between total
correlations and the sum of classical and quantum correlations obtained using
relative-entropy--based quantifiers.
