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<p>This work investigates the topological structure of multipartite entanglement in symmetric Dicke states <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(|D_n^{(k)}\rangle \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mo stretchy="false">|</mo> </mrow> <msubsup> <mi>D</mi> <mi>n</mi> <mrow> <mo stretchy="false">(</mo> <mi>k</mi> <mo stretchy="false">)</mo> </mrow> </msubsup> <mrow> <mo stretchy="false">⟩</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. By viewing qubits as topological loops, we establish a direct correspondence between the recursive measurement dynamics of Dicke states and the stability of <i>n</i>-Hopf links. We utilize the Schmidt rank to quantify bipartite entanglement resilience and introduce the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(l_1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>l</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>-norm of quantum coherence as a measure of <i>link fluidity</i>. We demonstrate that unlike fragile states such as <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\( \left| GHZ \right\rangle \)</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close="〉" open="|"> <mi>G</mi> <mi>H</mi> <mi>Z</mi> </mfenced> </math></EquationSource> </InlineEquation> (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.</p>

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

  • 期刊论文

  • 发表日期：

    2026年3月18日

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  • Sougata Bhattacharyya,
  • Sovik Roy

摘要

This work investigates the topological structure of multipartite entanglement in symmetric Dicke states \(|D_n^{(k)}\rangle \) | 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 \(l_1\) l 1 -norm of quantum coherence as a measure of link fluidity. We demonstrate that unlike fragile states such as \( \left| GHZ \right\rangle \) G H Z (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.