  Since the dawn of quantum theory, coherence was attributed as a key to
understand the weirdness of fundamental concepts like the wave-particle duality
and the Stern-Gerlach experiment. Recently, based on a resource theory
approach, the notion of quantum coherence was revisited and a plethora of
coherence quantifiers were proposed. In this work, we address this issue using
the language of coherence orders, developed by the NMR community. This allowed
us to investigate the role played by different subspaces of the Hilbert-Schmidt
space into physical processes and quantum protocols. We found some links
between decoherence and each coherence order. Moreover, we propose a sufficient
and straightforward criterion to testify the usefulness of a given state for
quantum enhanced phase estimation, relying on a minimal set of elements
belonging to the density matrix.
