Entanglement, Coherence, and Recursive Linking in Dicke states : A Topological Perspective

This work investigates the topological structure of multipartite entanglement in symmetric Dicke states $\mathrm{\mid }{D}_n^{(k)}⟩$. By viewing qubits as topological loops, we establish a direct correspondence between the recursive measurement dynamics of Dicke states and the stability of $n$-Hopf links. We utilize the Schmidt rank to quantify bipartite entanglement resilience and introduce the $l_1$-norm of quantum coherence as a measure of link fluidity. We demonstrate that unlike fragile states such as $\mid GHZ⟩$ (analogous to Borromean rings), Dicke states exhibit a robust, self-similar topology where local measurements preserve the global linking structure through non-vanishing residual coherence.