Quantifying coherence with respect to general quantum measurements

Coherence is a cornerstone of quantum theory and prerequisite for the advantage technologies. In recent work, notion coherence with respect to general measurement, i.e., positive operator-valued measure (POVM), was introduced embedded into resource-theoretic framework that generalizes standard resource coherence. particular, POVM-incoherent (free) states operations were established. this we explore features which arise due rich structure POVMs compared projective measurements. Moreover, introduce rigorous, probabilisitic POVM-based measures free operations. This leads introduction strongly monotonic neatly generalize well-known measures. Finally, show relative entropy POVM equal cryptographic randomness gain, providing an important operational meaning concept measurement.