  The quantum entropic uncertainty relation and entanglement witness in the
two-atom system coupling with the non-Markovian environments are studied by the
time-convolutionless master-equation approach. The influence of non-Markovian
effect and detuning on the lower bound of the quantum entropic uncertainty
relation and entanglement witness is discussed in detail. The results show
that, only if the two non-Markovian reservoirs are identical, increasing
detuning and non-Markovian effect can reduce the lower bound of the entropic
uncertainty relation, lengthen the time region during which the entanglement
can be witnessed, and effectively protect the entanglement region witnessed by
the lower bound of the entropic uncertainty relation. The results can be
applied in quantum measurement, quantum cryptography task and quantum
information processing.
