Localization of joint quantum measurements on $\mathbb{C}^d \otimes \mathbb{C}^d$ by entangled resources with Schmidt number at most $d$
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Quantum Physics arXiv:2601.02660 (quant-ph) [Submitted on 6 Jan 2026] Title:Localization of joint quantum measurements on $\mathbb{C}^d \otimes \mathbb{C}^d$ by entangled resources with Schmidt number at most $d$ Authors:Seiseki Akibue, Jisho Miyazaki View a PDF of the paper titled Localization of joint quantum measurements on $\mathbb{C}^d \otimes \mathbb{C}^d$ by entangled resources with Schmidt number at most $d$, by Seiseki Akibue and 1 other authors View PDF HTML (experimental) Abstract:Localizable measurements are joint quantum measurements that can be implemented using only non-adaptive local operations and shared entanglement. We provide a protocol-independent characterization of localizable projection-valued measures (PVMs) by exploiting algebraic structures that any such measurement must satisfy. We first show that a rank-1 PVM on $\mathbb{C}^d\otimes\mathbb{C}^d$ containing an element with the maximal Schmidt rank can be localized using entanglement of a Schmidt number at most $d$ if and only if it forms a maximally entangled basis corresponding to a nice unitary error basis. This reveals strong limitations imposed by non-adaptive local operations, in contrast to the adaptive setting where any joint measurement is implementable. We then completely characterize two-qubit rank-1 PVMs that can be localized with two-qubit entanglement, resolving a conjecture of Gisin and Del Santo, and finally extend our characterization to ideal two-qudit measurements, strengthening earlier results. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2601.02660 [quant-ph] (or arXiv:2601.02660v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.02660 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Seiseki Akibue [view email] [v1] Tue, 6 Jan 2026 02:18:17 UTC (4,351 KB) Full-text links: Access Paper: View a PDF of the paper titled Localization of joint quantum measurements on $\mathbb{C}^d \otimes \mathbb{C}^d$ by entangled resources with Schmidt number at most $d$, by Seiseki Akibue and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 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?)