Entanglement witness and entropy uncertainty of an open quantum system under the Zeno effect

In this paper, a two-level atom coupled with a double Lorentzian spectrum is solved by pseudomode theory, and an analytic representation of the density operator is obtained. Second, the paper investigates the entanglement witness and entropy uncertainty, and gets the analytical representation of entanglement, uncertainty, and their relationship. The environmental effects of the double Lorentzian spectrum are explained by non-Markovianity. In addition, this paper studies the influence of the Zeno effect on entanglement witness and uncertainty. The results show that the Zeno effect not only can 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.