This work establishes a direct operational connection between the entanglement structures of specific three-qubit states (i.e., multipartite entanglement) and their corresponding topological links. We investigate the symmetric \(\mid W\overline{W} \rangle \) state and the asymmetric \(\mid \text {Star} \rangle \) state through local projective measurements on individual qubits. The post-measurement states are analyzed via their Schmidt rank to characterize residual bipartite entanglement. For the symmetric \(\mid W\overline{W} \rangle \) state, measurement of any qubit consistently results in a non-maximally entangled post-measurement state (Schmidt rank 2), analogous to the behavior of a 3-Hopf link structure, where cutting any ring leaves the remaining two nontrivially linked. On the other hand, the \(\mid \text {Star} \rangle \) state exhibits a context-dependent fragility. Its behavior predominantly mirrors that of a 3-link chain where severing the central qubit decouples the system, while cutting an outer qubit often preserves a residual link. Crucially, for specific measurement outcomes, the \(\mid \text {Star} \rangle \) state also exhibits the defining property of the Borromean rings, where the loss of one qubit completely disentangles the remaining two. This analysis provides a concrete interpretation of topological linking structures as a resource for characterizing distributed entanglement and its resilience under local measurement operations, revealing that a single quantum state can contextually embody multiple distinct topological analogues.
