From vanishing pairwise entanglement to global separability:Entanglement structure and measures in the W subspace

Abstract:The $W$ subspace is defined as the subspace of the $n$-qubit Hilbert space spanned by states containing at most one excitation. In this work, a separability criterion is established for pure and mixed states supported in this subspace: if all reduced two-qubit subsystems are separable, then the entire $n$-qubit state is necessarily separable. This result motivates the identification of the sum of two-tangles as an entanglement measure for pure states supported in the $W$ subspace. Furthermore, it is shown that the commonly used $\pi$-tangle becomes ineffective for the $n$-qubit $W$ state as the system size increases, and vanishes in the large-$n$ limit. To address this limitation, the sum of $\pi$-tangles is introduced, which, like the sum of two-tangles, successfully quantifies the entanglement of the $n$-qubit $W$ state in the large-$n$ limit. In addition, a new condition for entanglement measures is introduced, which facilitates the formulation of a well-behaved and physically meaningful entanglement measure.

arXiv:2512.14566 [quant-ph]

(or arXiv:2512.14566v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2512.14566 Focus to learn more arXiv-issued DOI via DataCite

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