Robust Quantum Extremal Numbers

Quantum Physics arXiv:2608.13907 (quant-ph) [Submitted on 14 Aug 2026] Title:Robust Quantum Extremal Numbers Authors:Wanchen Zhang, Zicheng Han, Xiande Zhang View a PDF of the paper titled Robust Quantum Extremal Numbers, by Wanchen Zhang and 1 other authors View PDF HTML (experimental) Abstract:Absolutely maximally entangled states require every reduction of at most half of the parties to be maximally mixed, a condition that is both rigid and often impossible for qubit systems. Previous work introduced the quantum extremal number, which maximizes the number of exactly maximally mixed half-body marginals, and determined the exact value Qex(8,4)=56. The present work develops a robust extension of this extremal problem. For a subsystem $A$, the marginal maximal-mixing defect is defined by \[ D_A=2^{|A|}\operatorname{Tr}(\rho_A^2)-1 =2^{|A|}\left\|\rho_A-\frac{I_A}{2^{|A|}}\right\|_2^2, \] and $Q_{\mathrm{ex},\varepsilon}^{D}(n,k)$ is defined as the maximum number of $k$-body marginals satisfying $D_A\leq\varepsilon$ in an $n$-qubit pure state. This counting problem differs from approximate $k$-uniformity, which requires all $k$-body marginals to obey a common error bound. For pure states on $4m$ qubits, the following local stability inequality is established: \[ \sum_{i\in T}D_{T\setminus\{i\}}\geq1 \qquad (|T|=2m+1). \] It follows that, whenever $\varepsilon new | recent | 2026-08 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?)