Pauli Measurements Are Near-Optimal for Pure State Tomography
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Quantum Physics arXiv:2601.04444 (quant-ph) [Submitted on 7 Jan 2026] Title:Pauli Measurements Are Near-Optimal for Pure State Tomography Authors:Sabee Grewal, Meghal Gupta, William He, Aniruddha Sen, Mihir Singhal View a PDF of the paper titled Pauli Measurements Are Near-Optimal for Pure State Tomography, by Sabee Grewal and 3 other authors View PDF Abstract:We give an algorithm for pure state tomography with near-optimal copy complexity using single-qubit measurements. Specifically, given $\widetilde{O}(2^n/\epsilon)$ copies of an unknown pure $n$-qubit state $\lvert\psi\rangle$, the algorithm performs only \textit{nonadaptive Pauli measurements}, runs in time $\mathrm{poly}(2^n,1/\epsilon)$, and outputs $\lvert \widehat{\psi} \rangle$ that has fidelity $1-\epsilon$ with $\lvert \psi \rangle$ with high probability. This improves upon the previous best copy complexity bound of $\widetilde{O}(3^n/\epsilon)$. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2601.04444 [quant-ph] (or arXiv:2601.04444v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.04444 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Meghal Gupta [view email] [v1] Wed, 7 Jan 2026 23:16:37 UTC (26 KB) Full-text links: Access Paper: View a PDF of the paper titled Pauli Measurements Are Near-Optimal for Pure State Tomography, by Sabee Grewal and 3 other authorsView PDFTeX 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?)