The typicality of symmetry-induced entanglement

Quantum Physics [Submitted on 21 Mar 2026] The typicality of symmetry-induced entanglement Christian Boudreault, Nicolas Levasseur In the presence of a globally conserved charge N, a natural question is whether a given separable state can be separated into charge-conserving components. We dub this problem the Symmetric Separability Problem (SSP). On random states, the SSP is answered negatively with probability one for almost all N. Using a witness to the failure of symmetric separability, namely the number entanglement (NE) introduced in arXiv:2110.09388, we show that most symmetric and separable states are actually far from being symmetrically separable, with the NE featuring Gaussian concentration around a strictly positive mean value. We discuss some consequences of our results for quantum tasks in the presence of a superselection rule or in the absence of a common reference frame. Progress is made on the question of the size of the separable space constrained by N. We also touch upon the question of the complexity of SSP, and multiparty entanglement. Comments: Main text: 9 pages, 3 figures. Appendix: 12 pages, 3 figures Subjects: Quantum Physics (quant-ph); Other Condensed Matter (cond-mat.other) Cite as: arXiv:2603.20786 [quant-ph]   (or arXiv:2603.20786v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.20786 Focus to learn more Submission history From: Christian Boudreault [view email] [v1] Sat, 21 Mar 2026 12:24:08 UTC (486 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: cond-mat cond-mat.other 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?)