2025/09/07 by Bhattacharyya, Sougata, Roy, Sovik · 1 citation
#FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2509.05972
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 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 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 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.