Threshold entanglement sharing: quantum states with absolutely separable marginals

Quantum Physics [Submitted on 14 Apr 2026] Threshold entanglement sharing: quantum states with absolutely separable marginals Albert Rico, Jofre Abellanet-Vidal, Naga Bhavya Teja Kothakonda, Anna Sanpera, Gerard Anglès Munné 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 Submission history From: Jofre Abellanet-Vidal [view email] [v1] Tue, 14 Apr 2026 18:00:05 UTC (30 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)