On flavor-mass majorization uncertainty relations and their links to the mixing matrix

Abstract

We consider uncertainties in the case of flavor and mass eigenstates of neutrinos from the viewpoint of majorization uncertainty relations. Nontrivial lower bounds are a reflection of the fact that neutrinos cannot be simultaneously in a flavor and mass eigenstate. As quantitative measures of uncertainties, both the R\'{e}nyi and Tsallis entropies are utilized. In a certain sense, majorization uncertainty relations are directly connected to measurement statistics. On the other hand, magnitudes of elements of the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix are not known exactly. Hence, some conditions on applications of majorization uncertainty relations follow. We also discuss the case with detection inefficiencies, since it can naturally be incorporated into the entropic framework. Finally, some comments on applications of entropic uncertainty relations with quantum memory are given. The latter may be used in entanglement-assisted studying parameters of three-flavor neutrino oscillations.