Universal Sample Complexity Bounds in Quantum Learning Theory via Fisher Information matrix
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Quantum Physics arXiv:2602.21510 (quant-ph) [Submitted on 25 Feb 2026] Title:Universal Sample Complexity Bounds in Quantum Learning Theory via Fisher Information matrix Authors:Hyukgun Kwon, Seok Hyung Lie, Liang Jiang View a PDF of the paper titled Universal Sample Complexity Bounds in Quantum Learning Theory via Fisher Information matrix, by Hyukgun Kwon and 2 other authors View PDF HTML (experimental) Abstract:In this work, we show that the sample complexity (equivalently, the number of measurements) required in quantum learning theory within a general parametric framework, is fundamentally governed by the inverse Fisher information matrix. More specifically, we derive upper and lower bounds on the number of samples required to estimate the parameters of a quantum system within a prescribed small additive error and with high success probability under maximum likelihood estimation. The upper bound is governed by the supremum of the largest diagonal entry of the inverse Fisher information matrix, while the lower bound is characterized by any diagonal element evaluated at arbitrary parameter values. We then apply the general bounds to Pauli channel learning and to the estimation of Pauli expectation values in the asymptotic small-error regime, and recover the previously established sample complexity through considerably streamlined derivations. Furthermore, we identify the structural origin of exponential sample complexity in Pauli channel learning without entanglement and in Pauli expectation value estimation without quantum memory. We then extend the analysis to an error criterion based on the Euclidean distance between the true parameter values and their estimators. We derive the corresponding upper and lower bounds on the sample complexity, which are likewise characterized by the inverse Fisher information matrix. As an application, we consider Pauli expectation estimation with entangled probes. Finally, we highlight two fundamental contributions to quantum learning theory. First, we establish a systematic framework that determines the task-independent sample complexity under maximum-likelihood estimation. Second, we show that, in the small-error regime, learning sample complexity is governed by the inverse Fisher information matrix. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2602.21510 [quant-ph] (or arXiv:2602.21510v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.21510 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Hyukgun Kwon [view email] [v1] Wed, 25 Feb 2026 02:51:49 UTC (373 KB) Full-text links: Access Paper: View a PDF of the paper titled Universal Sample Complexity Bounds in Quantum Learning Theory via Fisher Information matrix, by Hyukgun Kwon and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 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?)