Symmetric and asymmetric tripartite states under the lens of entanglement splitting and topological linking

• URL: http://arxiv.org/abs/2509.05972v1
• Date: Sun, 07 Sep 2025 08:32:06 GMT
• Title: Symmetric and asymmetric tripartite states under the lens of entanglement splitting and topological linking
• Authors: Sougata Bhattacharyya, Sovik Roy,
• Abstract summary: We investigate the symmetric $wwbar$ state and the asymmetric $starstate$ state through local projective measurements on individual qubits.<n>For the symmetric $wwbar$ state, measurement of any qubit consistently results in a non-maximally entangled post-measurement state.<n>For the asymmetric $starstate$ state, the loss of one qubit completely disentangles the remaining two.
• Score: 0.0
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: 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 $\wwbar$ state and the asymmetric $\starstate$ 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 $\wwbar$ state, measurement of any qubit consistently results in a non-maximally entangled post-measurement state (Schmidt rank 2), analogous to the behavior of a \textit{3-Hopf link} structure, where cutting any ring leaves the remaining two nontrivially linked. On the other hand, the $\starstate$ state exhibits a context-dependent fragility. Its behavior predominantly mirrors that of a \textit{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 $\starstate$ state also exhibits the defining property of the \textit{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.

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