# Flavor-mass majorization uncertainty relations and their links to the mixing matrix

## TL;DR

This paper develops majorization-based uncertainty relations for neutrino flavor and mass states using entropic measures, linking the bounds to the neutrino mixing matrix and considering detection inefficiencies.

## Contribution

It introduces majorization uncertainty relations for neutrino states using Rényi and Tsallis entropies, connecting bounds to mixing angles and incorporating detection inefficiencies.

## Key findings

- Majorization bounds depend on mixing angles θ12 and θ13.
- Entropic uncertainty relations are applicable similarly to Maassen-Uffink.
- Detection inefficiencies can be integrated into the entropic framework.

## Abstract

Uncertainties in flavor and mass eigenstates of neutrinos are considered within the majorization approach. Nontrivial bounds reflect the fact that neutrinos cannot be simultaneously in flavor and mass eigenstates. As quantitative measures of uncertainties, both the R\'{e}nyi and Tsallis entropies are utilized. Within the current amount of experience concerning the mixing matrix, majorization uncertainty relations need to put values of only two parameters, viz. $\theta_{12}$ and $\theta_{13}$. That is, the majorization approach is applicable within the same framework as the Maassen-Uffink relation recently utilized in this context. We also consider the case of detection inefficiencies, since it can naturally be incorporated into the entropic framework. Short comments on applications of entropic uncertainty relations with quantum memory are given.