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In this paper we derive a new quantum entropic uncertainty relation, boundingthe conditional smooth quantum min entropy based on the result of a measurementusing a two outcome POVM and the failure probability of a classical samplingstrategy. Our relation works for systems of arbitrary finite dimension. Weapply it to analyze a new source independent quantum random number generationprotocol and show our relation provides optimistic results compared to priorwork.

A New High-Dimensional Quantum Entropic Uncertainty Relation with Applications