Local Distinguishability of Multipartite Orthogonal Quantum States: Generalized and Simplified
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Quantum Physics arXiv:2601.20074 (quant-ph) [Submitted on 27 Jan 2026] Title:Local Distinguishability of Multipartite Orthogonal Quantum States: Generalized and Simplified Authors:Ian George, Mohammad A. Alhejji View a PDF of the paper titled Local Distinguishability of Multipartite Orthogonal Quantum States: Generalized and Simplified, by Ian George and Mohammad A. Alhejji View PDF HTML (experimental) Abstract:In a seminal work [PRL85.4972], Walgate, Short, Hardy, and Vedral prove in finite dimensions that for every pair of pure multipartite orthogonal quantum states, there exists a one-way local operations and classical communication (LOCC) protocol that perfectly distinguishes the pair. We extend this result to infinite dimensions with a simpler proof. For states on $\mathbb{C}^{d_A \times d_A} \otimes \mathbb{C}^{d_B \times d_B}$, we strengthen this existence result by constructing an $O(d_A^2 d_B^2)$-time algorithm that specifies such a perfect one-way LOCC protocol. Finally, we establish the equivalence between Walgate et al.'s result and the fact that the one-shot environment-assisted classical capacity of every quantum channel is at least 1 bit per channel use, thereby clarifying the literature on these notions. At the core of all of these results is the fact that every operator with vanishing trace admits a basis where its diagonal entries are all zero. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2601.20074 [quant-ph] (or arXiv:2601.20074v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.20074 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Ian George [view email] [v1] Tue, 27 Jan 2026 21:36:27 UTC (127 KB) Full-text links: Access Paper: View a PDF of the paper titled Local Distinguishability of Multipartite Orthogonal Quantum States: Generalized and Simplified, by Ian George and Mohammad A. AlhejjiView 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?)