• Accepted Paper

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

Reza Hamzehofi

Phys. Rev. A - Accepted 1 October, 2026

DOI: https://doi.org/10.1103/qznr-1gpr

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 π-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 π-tangles is introduced, which, like the sum of two-tangles, successfully quantifiesthe 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.

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