Entropic Uncertainty Relations for (N, M)-POVMs

Abstract

Characterizing uncertainty relations through entropy is a hot topic in quantum information theory. In this paper, the multifarious lower entropic bounds, which can unify the existing entropic uncertainty relations, are derived, including the Tsallis entropies, the Rényi entropies, the min-entropies and the Maassen-Uffink type based on a broad family of generalized informationally complete symmetric measurements. Furthermore, some detailed examples are given and it is shown that the presented entropic uncertainty relations are more powerful and comprehensive than the existing ones.