Tripartite Entanglement Dynamics in the presence of Non-Markovian Environment

We study on the tripartite entanglement dynamics when each party is initially entangled with other parties, but they locally interact with their own non-Markovian environment. First, we consider three GHZ-type initial states, all of which have GHZ symmetry provided that the parameters are chosen appropriately. However, this symmetry is broken due to the effect of environment. The corresponding $\pi$-tangles, one of the tripartite entanglement measure, are analytically computed at arbitrary time. The revival phenomenon of entanglement occurs after complete disappearance of entanglement. We also consider two W-type initial states. The revival phenomenon also occurs in this case. On the analytical ground the robustness issue against the effect of environment is examined for both GHZ-type and W-type initial states.