Quantifying Unxtendibility via Virtual State Extension

Quantum Physics arXiv:2510.24895 (quant-ph) [Submitted on 28 Oct 2025] Title:Quantifying Unxtendibility via Virtual State Extension Authors:Hongshun Yao, Jingu Xie, Xuanqiang Zhao, Chengkai Zhu, Ranyiliu Chen, Xin Wang View a PDF of the paper titled Quantifying Unxtendibility via Virtual State Extension, by Hongshun Yao and Jingu Xie and Xuanqiang Zhao and Chengkai Zhu and Ranyiliu Chen and Xin Wang View PDF HTML (experimental) Abstract:The monogamy of entanglement, which restricts how entanglement can be shared among multiple parties, provides a powerful lens through which to characterize its structure, often formalized through the concept of symmetric extendibility. In this work, we propose a novel, operational viewpoint to quantify the degree to which a state is not extendible by introducing a virtual state extension task. We define the virtual extension cost as the minimum simulation cost of a non-physical protocol that satisfies the marginal conditions of a $k$-extension. We derive an exact, closed-form expression for this cost for the important family of isotropic states. Our central result establishes a profound connection between entanglement theory and quantum communication theory: the virtual extension cost of a maximally entangled state is precisely equal to the optimal simulation cost of universal virtual quantum broadcasting. Leveraging the algebraic machinery of the partially transposed permutations matrix algebra, we find an analytical formula for this cost and construct an explicit quantum circuit for the optimal broadcasting protocol, thereby resolving an open question. Furthermore, we demonstrate the connection between the virtual extension cost and the absolute robustness of unextendibility, thus endowing the latter with a clear operational meaning. We also show the natural properties of virtual extension cost as an entanglement measure, including its role as a bound for entanglement distillation and its relationship with logarithmic negativity. Our findings unify disparate concepts and offer a new perspective on entanglement quantification. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2510.24895 [quant-ph] (or arXiv:2510.24895v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2510.24895 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Ranyiliu Chen [view email] [v1] Tue, 28 Oct 2025 18:57:17 UTC (290 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantifying Unxtendibility via Virtual State Extension, by Hongshun Yao and Jingu Xie and Xuanqiang Zhao and Chengkai Zhu and Ranyiliu Chen and Xin WangView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-10 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)