  Finite tight frames are interesting in various topics including questions of
quantum information. Each complex tight frame leads to a resolution of the
identity in the Hilbert space. Symmetric informationally complete measurements
are a special class of equiangular tight frames. Applications of such frames in
quantum physics deserve more attention than they have obtained. We derive
uncertainty relations for a quantum measurement assigned to an equiangular
tight frame. Main results follow from estimation of the corresponding index of
coincidence. State-dependent and state-independent formulations are both
addressed. Also, we discuss applications of considered measurements to detect
entanglement and other correlations.
