Separability Criteria of Quantum States based on Generalized Bloch Representation

Quantum Physics arXiv:2510.24110 (quant-ph) [Submitted on 28 Oct 2025] Title:Separability Criteria of Quantum States based on Generalized Bloch Representation Authors:Linwei Li, Hongmei Yao, Chunlin Yang, Shaoming Fei View a PDF of the paper titled Separability Criteria of Quantum States based on Generalized Bloch Representation, by Linwei Li and Hongmei Yao and Chunlin Yang and Shaoming Fei View PDF HTML (experimental) Abstract:Quantum entanglement serves as a fundamental resource in quantum information theory. This paper presents a comprehensive framework of separability criteria for detecting entanglement across quantum systems, from bipartite to multipartite states. We propose a novel unified parameterized extended correlation tensor, constructed via the generalized Bloch representation under an arbitrary orthogonal basis, which bridges our bipartite criterion with several existing ones. Moreover, we develop a specialized tensor unfolding technique -- termed mixed mode matrix unfolding -- that naturally generalizes the conventional $k$-mode matrix unfolding and enables the generalization of the extended correlation tensor construction to multipartite systems. And we derive several separability criteria for multipartite states. Numerical examples demonstrate that our separability criteria exhibit enhanced capability in detecting entanglement. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2510.24110 [quant-ph] (or arXiv:2510.24110v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2510.24110 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Hongmei Yao [view email] [v1] Tue, 28 Oct 2025 06:29:06 UTC (3,211 KB) Full-text links: Access Paper: View a PDF of the paper titled Separability Criteria of Quantum States based on Generalized Bloch Representation, by Linwei Li and Hongmei Yao and Chunlin Yang and Shaoming FeiView 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?)