Coherence orders, decoherence, and quantum metrology

Since the dawn of quantum theory, coherence has been attributed as a key to understand the weirdness of fundamental concepts such as, e.g., 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 was proposed. In this work, we address such issues employing 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 method to testify to the usefulness of a given state for quantum enhanced phase estimation, relying on a minimal set of elements belonging to the density matrix.