Two novel pure-state coherence measures in quantifying coherence

Abstract: 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.