  In the resource theory of coherence, the quantification of quantum-state
coherence is an important task. In this regard, the key ingredients are the
various coherence monotones (or measures). There are few coherence-monotone
classes that solely depend on other coherence measures defined for all the pure
states; in other words, they rely on the pure state coherence measures (PSCM).
Here, we set forth two such novel PSCMs, and validate each of them through the
fulfillment of all four necessary conditions. In addition, we delve into the
most recent (as per our knowledge) coherence-monotone class based on the
innovative idea of quantifying coherence in terms of pure-state coherence,
further redefine it, and, through the study of convexity under mixing, justify
why this coherence monotone class cannot be treated as a coherence-measure
class in general.
