Uncertainty relations based on mutually unbiased measurements
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 Rnyi and Tsallis entropies.
uncertainty relations mutually unbiased measurements index of coincidence rnyi and tsallis entropies