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 is an element of(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.