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Robustness of Greenberger-Horne-Zeilinger and W states against Dzyaloshinshkii-Moriya interaction

In this article the robustness of tripartite Greenberger-Horne-Zeilinger (GHZ) and W states is investigated against Dzyaloshinskii-Moriya (i.e. DM) interaction. We consider a closed system of three qubits and an environmental qubit. The environmental qubit interacts with any one of the three qubits through DM interaction. The tripartite system is initially prepared in GHZ and W states respectively. The composite four qubits system evolve with unitary dynamics. We detach the environmental qubit by tracing out from four qubits and profound impact of DM interaction is studied on the initial entanglement of the system. As a result we find that the bipartite partitions of W states suffer from entanglement sudden death (i.e. ESD), while tripartite entanglement does not. On the other hand bipartite partitions and tripartite entanglement in GHZ states does not feel any influence of DM interaction. So, we find that GHZ states have robust character than W states. In this work we consider generalised GHZ and W states and three $π$ is used as an entanglement measure. This study can be useful in quantum information processing where unwanted DM interaction takes place.