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

[2512.14566] From vanishing pairwise entanglement to global separability:Entanglement structure and measures in the W subspace Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Quantum Physics arXiv:2512.14566 (quant-ph) [Submitted on 16 Dec 2025 ( v1 ), last revised 15 Aug 2026 (this version, v2)] Title: From vanishing pairwise entanglement to global separability:Entanglement structure and measures in the W subspace Authors: Reza Hamzehofi View a PDF of the paper titled From vanishing pairwise entanglement to global separability:Entanglement structure and measures in the W subspace, by Reza Hamzehofi View PDF 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. Subjects: Quantum Physics (quant-ph) Cite as: 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 Submission history From: Reza Hamzehofi [ view email ] [v1] Tue, 16 Dec 2025 16:37:21 UTC (674 KB) [v2] Sat, 15 Aug 2026 06:50:23 UTC (1,030 KB) Full-text links: Access Paper: View a PDF of the paper titled From vanishing pairwise entanglement to global separability:Entanglement structure and measures in the W subspace, by Reza Hamzehofi View PDF view license Current browse context: quant-ph < prev | next > new | recent | 2025-12 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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