Threshold entanglement sharing: quantum states with absolutely separable marginals
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Quantum Physics arXiv:2604.13169 (quant-ph) [Submitted on 14 Apr 2026] Title:Threshold entanglement sharing: quantum states with absolutely separable marginals Authors:Albert Rico, Jofre Abellanet-Vidal, Naga Bhavya Teja Kothakonda, Anna Sanpera, Gerard Anglès Munné View a PDF of the paper titled Threshold entanglement sharing: quantum states with absolutely separable marginals, by Albert Rico and 4 other authors View PDF HTML (experimental) Abstract:Motivated to understand how entanglement resources can be distributed in quantum networks, we introduce threshold entanglement (TE) states. These are multipartite quantum states whose entanglement across bipartitions forces all marginals of half or less local systems to be (absolutely) separable. First, in contrast to states used for quantum secret sharing, we demonstrate that TE states exist for four and seven qubits. Second, between four and nine qubits, we delimit the average entanglement that TE states must have by combining two semidefinite programming relaxations: (i) lower bounds on the minimal purity of pure state marginals, and (ii) upper bounds on the maximal purity of mixed absolutely separable states. Besides delimiting the existence regions of TE states, our approach independently improves the best known bounds on both of the above problems. Moreover, these improved bounds show that TE states of eight qubits cannot exist. Numerical evidence suggests that TE states accommodate significant amounts of entanglement and magic, which are resources needed for quantum advantage in quantum computing. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.13169 [quant-ph] (or arXiv:2604.13169v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.13169 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Jofre Abellanet-Vidal [view email] [v1] Tue, 14 Apr 2026 18:00:05 UTC (30 KB) Full-text links: Access Paper: View a PDF of the paper titled Threshold entanglement sharing: quantum states with absolutely separable marginals, by Albert Rico and 4 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADSGoogle 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?)