Uncertainty relations for quantum measurements assigned to the conical 2-designs

This study investigates the uncertainty relations based on quantum measurements assigned to conical 2-designs. A general relation is formulated based on the conical 2-designs formed by quantum measurements and the corresponding index of coincidence. The relation is employed to derive novel Tsallis and R & eacute;nyi a-entropic uncertainty relations and fine-grained uncertainty relations. Furthermore, the proposed entropic uncertainty relation is applied to quantum steering. It is demonstrated that the findings provide a tighter entropic lower bound, generalizing and improving some existing results in the literature.