Bounding the entanglement of a state from its spectrum

Quantum Physics [Submitted on 2 Apr 2026] Bounding the entanglement of a state from its spectrum Jofre Abellanet-Vidal, Guillem Müller-Rigat, Albert Rico, Anna Sanpera Recent efforts have focused on characterizing the set of separable states that cannot be made entangled by any global unitary transformation. Here we characterize the set of states whose entanglement content cannot be increased under any unitary. By employing linear maps (and their inverses), we derive constraints on the achievable degree of entanglement from the spectrum of the density matrix. In particular, we focus on the negativity and the Schmidt number. Our approach yields analytical and practical criteria for quantifying the entanglement content of full-rank states in arbitrary dimensions using only a subset of their eigenvalues. Moreover, some of the derived conditions can be used to bound the spectra of Schmidt number witnesses. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.02420 [quant-ph]   (or arXiv:2604.02420v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.02420 Focus to learn more Submission history From: Jofre Abellanet-Vidal [view email] [v1] Thu, 2 Apr 2026 18:00:04 UTC (467 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?)