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

TL;DR

This paper explores the topological structure of multipartite entanglement in symmetric Dicke states, linking quantum properties to topological links and demonstrating their robustness under measurements.

Contribution

It introduces a topological perspective on Dicke states, connecting recursive measurement dynamics to $n$-Hopf links and quantifying entanglement resilience with novel measures.

Findings

Dicke states correspond to stable $n$-Hopf links.

Local measurements preserve the linking structure in Dicke states.

Dicke states are more robust than GHZ states under measurements.

Abstract

This work investigates the topological structure of multipartite entanglement in symmetric Dicke states $|D_n^{(k)}\rangle$. 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 $ \left| GHZ \right \rangle$ (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.