Abstract
In this work, we investigate the dynamics of quantum-memory-assisted entropic uncertainty relation (EUR) and quantum correlation quantified by entropic discord and geometric discord within the Markovian reservoir and non-Markovian reservoir. Particularly, when the initial state is a pure sate or mixed state the EUR gradually increases during the evolution at first, but subsequently tends to stable in the long-time limit. On other hand, for the separable state the EUR almost keeps constant. In contrast, quantum discord decay asymptotically to zero for all types of initial states. As an application, we prove that both two quantum discords witnessed by the EUR are determined by the version of discord chosen, which regardless of the reservoir.
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