Entropic uncertainty relations for general symmetric informationally complete positive operator-valued measures and mutually unbiased measurements

We construct inequalities between R\'{e}nyi entropy and the indexes of coincidence probability distributions, based on which we obtain improved state-dependent entropic uncertainty relations for general symmetric informationally complete positive operator-valued measures (SIC-POVM) mutually unbiased measurements (MUM) finite dimensional systems. show that our SIC-POVMs MUMs can be tight sufficiently mixed states, moreover, comparisons to numerically optimal results are made via information diagrams.