  We formulate uncertainty relations for mutually unbiased bases and symmetric
informationally complete measurements in terms of the R\'{e}nyi and Tsallis
entropies. For arbitrary number of mutually unbiased bases in a
finite-dimensional Hilbert space, we give a family of Tsallis $\alpha$-entropic
bounds for $\alpha\in(0;2]$. Relations in a model of detection inefficiences
are obtained. In terms of R\'{e}nyi's entropies, lower bounds are given for
$\alpha\in[2;\infty)$. State-dependent and state-independent forms of such
bounds are both given. Uncertainty relations in terms of the min-entropy are
separately considered. We also obtain lower bounds in term of the so-called
symmetrized entropies. The presented results for mutually unbiased bases are
extensions of some bounds previously derived in the literature. We further
formulate new properties of symmetric informationally complete measurements in
a finite-dimensional Hilbert space. For a given state and any SIC-POVM, the
index of coincidence of generated probability distribution is exactly
calculated. Short notes are made on potential use of this result in
entanglement detection. Further, we obtain state-dependent entropic uncertainty
relations for a single SIC-POVM. Entropic bounds are derived in terms of the
R\'{e}nyi $\alpha$-entropies for $\alpha\in[2;\infty)$ and the Tsallis
$\alpha$-entropies for $\alpha\in(0;2]$. In the Tsallis formulation, a case of
detection inefficiences is briefly mentioned. For a pair of symmetric
informationally complete measurements, we also obtain an entropic bound of
Maassen-Uffink type.
