Estimating coherence with respect to general quantum measurements

The conventional coherence is defined with respect to a fixed orthonormal basis, i.e., von Neumann measurement. Recently, generalized quantum general positive operator-valued measurements has been presented. Several well-defined measures, such as the relative entropy of $$C_{r}$$ , $$l_{1}$$ norm $$C_{l_{1}}$$ and $$C_{T,\alpha }$$ based on Tsallis POVMs have obtained. In this work, we investigate properties . We estimate upper bounds ; show that minimal error probability least square measurement state discrimination given by $$C_{T,1/2}$$ derive uncertainty relations calculate average values over random pure states. All these results include corresponding special cases.