Tight Quantum Lower Bound for k-Distinctness
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Quantum Physics arXiv:2604.05133 (quant-ph) [Submitted on 6 Apr 2026] Title:Tight Quantum Lower Bound for k-Distinctness Authors:Aleksandrs Belovs View a PDF of the paper titled Tight Quantum Lower Bound for k-Distinctness, by Aleksandrs Belovs View PDF Abstract:In this paper, we introduce a new quantum query lower bound framework. It is inspired by Zhandry's compressed oracle technique, but it also subsumes the polynomial method as a special case. Compared to Zhandry's technique, our approach has two key differences. First, we do not use any oracles (except for the standard input oracle), and define ``knowledge'' directly through the expansion of the state of the algorithm in the Fourier basis. Second, we allow arbitrary probability distributions of inputs. We show how this framework behaves on the problem of finding equal elements in the input string. In particular, we demonstrate its power by proving a first tight quantum query lower bound for the k-Distinctness problem. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.05133 [quant-ph] (or arXiv:2604.05133v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.05133 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Aleksandrs Belovs [view email] [v1] Mon, 6 Apr 2026 19:52:58 UTC (53 KB) Full-text links: Access Paper: View a PDF of the paper titled Tight Quantum Lower Bound for k-Distinctness, by Aleksandrs BelovsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-04 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?)