Entanglement, coherence, and recursive linking in Dicke states: a topological perspective

Abstract

This work investigates the topological structure of multipartite entanglement in symmetric Dicke states |Dn(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 l1-norm of quantum coherence as a measure of link fluidity. We demonstrate that unlike fragile states such as 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. © The Author(s), under exclusive license to Chapman University 2026.