Uncertainty relations based on mutually unbiased measurements

Abstract: We derive uncertainty relation inequalities according to the mutually unbiased measurements. Based on the calculation of the index of coincidence of probability distribution given by $d+1$ MUMs on any density operator $\rho$ in $\mathbb{C}^{d}$, both state-dependent and state-independent forms of lower entropic bounds are given. Furthermore, we formulate uncertainty relations for MUMs in terms of R\'{e}nyi and Tsallis entropies.