Entanglement, anti-flatness, and nonlocal nonstabilizerness: a unified perspective from entanglement spectrum

Quantum Physics arXiv:2609.01993 (quant-ph) [Submitted on 2 Sep 2026] Title:Entanglement, anti-flatness, and nonlocal nonstabilizerness: a unified perspective from entanglement spectrum Authors:Lei-Yi-Nan Liu, Jian Cui View a PDF of the paper titled Entanglement, anti-flatness, and nonlocal nonstabilizerness: a unified perspective from entanglement spectrum, by Lei-Yi-Nan Liu and 1 other authors View PDF HTML (experimental) Abstract:Entanglement and nonstabilizerness capture distinct aspects of quantum complexity, yet their relation through the entanglement spectrum remains only partially understood. Here we develop a unified spectral framework for bipartite nonlocal nonstabilizerness. We introduce a generalized anti-flatness and derive universal upper and lower bounds on the nonlocal stabilizer Rényi entropy (SRE) in terms of Rényi entanglement entropy and spectral non-uniformity. We apply these bounds to exponentially and algebraically decaying spectra, revealing distinct relations between entanglement and nonlocal nonstabilizerness. For the marginal algebraic spectrum and the Calabrese--Lefevre spectrum, we further introduce a dyadic-shell sandwich construction that bounds the ordered entanglement spectrum by upper and lower shell-flat spectra and determines the asymptotic nonlocal SRE scaling. At one-dimensional conformal critical points, this yields a universal hierarchy of double-logarithmic scaling laws. Our spectral bounds and dyadic-shell sandwich construction provide general tools for analyzing nonlocal SRE, offering a flexible framework that can be applied to a wide range of entanglement spectra in quantum many-body systems. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2609.01993 [quant-ph] (or arXiv:2609.01993v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.01993 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Lei-Yi-Nan Liu [view email] [v1] Wed, 2 Sep 2026 02:00:20 UTC (371 KB) Full-text links: Access Paper: View a PDF of the paper titled Entanglement, anti-flatness, and nonlocal nonstabilizerness: a unified perspective from entanglement spectrum, by Lei-Yi-Nan Liu and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 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?)