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The quantum entropic uncertainty relation and entanglement witness in thetwo-atom system coupling with the non-Markovian environments are studied by thetime-convolutionless master-equation approach. The influence of non-Markovianeffect and detuning on the lower bound of the quantum entropic uncertaintyrelation and entanglement witness is discussed in detail. The results showthat, only if the two non-Markovian reservoirs are identical, increasingdetuning and non-Markovian effect can reduce the lower bound of the entropicuncertainty relation, lengthen the time region during which the entanglementcan be witnessed, and effectively protect the entanglement region witnessed bythe lower bound of the entropic uncertainty relation. The results can beapplied in quantum measurement, quantum cryptography task and quantuminformation processing.

The quantum entropic uncertainty relation and entanglement witness in the two-atom system coupling with the non-Markovian environments