Near-projective GHZ certification from disjoint Bell measurements
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Quantum Physics arXiv:2606.09947 (quant-ph) [Submitted on 8 Jun 2026] Title:Near-projective GHZ certification from disjoint Bell measurements Authors:Hyunho Cha, Jungwoo Lee View a PDF of the paper titled Near-projective GHZ certification from disjoint Bell measurements, by Hyunho Cha and 1 other authors View PDF HTML (experimental) Abstract:Certifying multipartite entangled states is a basic task in quantum information processing, but the achievable copy complexity depends crucially on the measurements available to the verifier. The strongest possible certification measurement for a known pure target state \(|\psi\rangle\) is the two-outcome projector \(\{|\psi\rangle\langle\psi|,\mathsf{I}-|\psi\rangle\langle\psi|\}\), which is copy-optimal but often experimentally unrealistic or outside the intended measurement model. In this work, we introduce Bell-Matching Certification (BM-Cert), a single-copy verification protocol for the \(n\)-qubit Greenberger--Horne--Zeilinger state using only disjoint two-qubit Bell-basis measurements, together with one single-qubit \(X\)-basis measurement when \(n\) is odd. Surprisingly, a simple combinatorial effect yields perfect completeness and a verification spectral gap \(\nu_\mathrm{BM}(n)=1-O(1/n)\), so the protocol approaches the ideal projective verification asymptotically as \(n\) grows. This contrasts with local Pauli GHZ verification, whose optimal spectral gap remains bounded away from \(1\). Thus, allowing only two-qubit entangling measurements on disjoint pairs is already enough to achieve asymptotically ideal projective certification. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2606.09947 [quant-ph] (or arXiv:2606.09947v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.09947 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Hyunho Cha [view email] [v1] Mon, 8 Jun 2026 07:23:17 UTC (13 KB) Full-text links: Access Paper: View a PDF of the paper titled Near-projective GHZ certification from disjoint Bell measurements, by Hyunho Cha and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 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?)