How to quantify coherence: Distinguishing speakable and unspeakable notions. I. Marvian and R. W. Spekkens in Phys. Rev. A 94:052324 (2016). What the paper says!?
This is a long text (the introduction alone is over 6 pages and is followed by a section "Preliminaries") that delves into the relevance of the theory of asymmetry (itself linked to the problem of quantum reference frames) into the problem of quantum resource theory.
In particular, it takes a detailed look at the issue that different choices of basis can be made for the incoherent states, making what is coherent, or resourceful, a seemingly vague notion. This point is also made by other authors but without contemplating the root of what this means. Here the Authors describe how the information can be "speakable", in the sense of being irrelevant to the final exploitation of the resource, or "unspeakable" if it is tightly linked to how the quantum coherence is to be processed.
There is a detailed list of applications of quantum coherence at the beginning.
This is an important text on an important underlying idea (being more fundamental than the standard quantum coherence approaches) which would need further attention.