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Protecting entanglement from decoherence is a critical aspect of quantuminformation processsing. For many-body quantum systems evolving underdecoherence, estimating multipartite entanglement is challenging. Thischallenge can be met up by considering distance based measure such as relativeentropy of entanglement which decisively measures entanglement in both pure aswell as mixed states. In this work, we investigate the tripartite entanglementdynamics of pure and mixed states in the presence of a structured dephasingenvironment at finite temperature. We show that the robustness of the quantumsystem to decoherence is dependent on the distribution of entanglement and itsrelation to different configurations of the bath. If the bath is structuredindividually such that each qubit has its own environment, the system hasdifferent dynamics compared to when the bath is common to all the three qubits.From the results we conjecture that there is a connection between thedistribution of entanglement among the qubits and the distribution of bathdegrees of freedom, and the interplay of these two distributions determines thedecay rate of the entanglement dynamics. The sustainability of tripartiteentanglement is shown to be enhanced significantly in presence of reservoirmemory.

Entanglement preservation in tripartite quantum systems under dephasing dynamics