Family of coherence measures and duality between quantum coherence and path distinguishability

Coherence measures and their operational interpretations lay the cornerstone of coherence theory. In this paper, we introduce a class of coherence measures with $\alpha$ affinity, say $\alpha$ affinity of coherence for $\alpha \in (0,1)$. Furthermore, we obtain the analytic formulas for these coherence measures and study their corresponding convex roof extension. We provide an operational interpretation for $1/2$ affinity of coherence by showing that it is equal to the error probability to discrimination a set of pure states with the least-square measurement. By employing this relationship we regain the optimal measurement for equiprobable quantum state discrimination. Moreover, we compare these coherence quantifiers and establish a complementarity relation between the $1/2$ affinity of coherence and path distinguishability for some special cases.