The entropic uncertainty principle in the form proven by Maassen and Uffink yields a fundamental inequality that is prominently used in many places all over the field of HAIR ACCESORIES STYLING KIT quantum information theory.In this paper, we provide a family of versatile generalizations of this relation.Our proof methods build on a deep connection between entropic uncertainties and interpolation inequalities for the doubly stochastic map that links probability distributions in two measurement bases.In contrast to the original relation, our generalization Cover Ups/Kimonos also incorporates the von Neumann entropy of the underlying quantum state.
These results can be directly used to bound the extractable randomness of a source-independent quantum random number generator in the presence of fully quantum attacks, to certify entanglement between trusted parties, or to bound the entanglement of a system with an untrusted environment.