Optimal min-entropy uncertainty relation
Phys. Rev. A 113, 022215 – Published 18 February, 2026
DOI: https://doi.org/10.1103/6yvn-hkqb
Abstract
Entropic uncertainty relations have been a famed research topic for over 65 years with many applications and still many unknowns left. For example, even for single-qubit states, the optimal min-entropy uncertainty relation has only been found for pure states. In this paper we provide the optimal min-entropy uncertainty relation for mixed states of any purity for pairs of arbitrary qudit bases, marking a significant milestone in this journey. Moreover, our proof of optimality is constructive: for every base overlap and state purity we find an explicit example that saturates our bound.
