Finite-Sample Selected Covariance Spectra in Classical Shadows
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Quantum Physics arXiv:2606.00527 (quant-ph) [Submitted on 30 May 2026] Title:Finite-Sample Selected Covariance Spectra in Classical Shadows Authors:Masahito Hayashi View a PDF of the paper titled Finite-Sample Selected Covariance Spectra in Classical Shadows, by Masahito Hayashi View PDF HTML (experimental) Abstract:We study finite-sample estimation of selected covariance matrices of classical-shadow outputs. For a general shadow-output vector, we consider its covariance matrix and a fixed selected compression. Our main theorem applies to arbitrary shadow protocols and gives an operator-norm error bound for the selected sample-centered empirical covariance. When the protocol-dependent constants appearing in this bound remain independent of the ambient system size, the required sample size is also independent of the ambient dimension. The proof combines matrix Bernstein concentration, an exact rank-one centering identity, and Weyl and Davis--Kahan perturbation bounds. We verify this bounded-output condition for local measurement settings. For general local product shadow protocols with fixed local dimension, finite-weight product observables lead to bounds controlled by support sizes and local reconstruction coefficients, not by the total number of tensor factors. Hence uniform bounds on selected set size, observable weight, and local reconstruction coefficients imply dimension-independent selected covariance estimation. For biased local Pauli shadows, we evaluate the relevant bound in closed form from the selected Pauli supports and local basis-selection probabilities. We also derive an exact covariance formula governed by Pauli compatibility and inverse-probability overlap factors, showing how measurement bias affects both diagonal variances and off-diagonal statistical couplings. A comparison with global Clifford shadows shows that this dimension-independent local behavior is not automatic for every shadow protocol. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2606.00527 [quant-ph] (or arXiv:2606.00527v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.00527 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Masahito Hayashi [view email] [v1] Sat, 30 May 2026 04:46:49 UTC (45 KB) Full-text links: Access Paper: View a PDF of the paper titled Finite-Sample Selected Covariance Spectra in Classical Shadows, by Masahito HayashiView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 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?)