Tight Quantum Lower Bound for k-Distinctness

Quantum Physics [Submitted on 6 Apr 2026] Tight Quantum Lower Bound for k-Distinctness Aleksandrs Belovs 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: 43 pages 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 Submission history From: Aleksandrs Belovs [view email] [v1] Mon, 6 Apr 2026 19:52:58 UTC (53 KB) Access Paper: view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)