  The entanglement witness and the entropy uncertainty are investigated by
using the pseudomode theory for the open two-atom system under the quantum Zeno
effect. The results show that, only when the two spectrums satisfy strong
coupling with the atom, the time of entanglement witness can be prolonged and
the lower bound of the entropic uncertainty can be reduced, and the
entanglement can be witnessed many times. We also gave the corresponding
physical explanation by the non-Markovianity. The Zeno effect not only can very
effectively prolong the time of entanglement witness and reduce the lower bound
of the entropy uncertainty, but also can greatly enhance the time of
entanglement witness and reduce the entanglement value of witness.
