Classical shadows with arbitrary group representations

Quantum Physics [Submitted on 1 Apr 2026] Classical shadows with arbitrary group representations Maxwell West, Frederic Sauvage, Aniruddha Sen, Roy Forestano, David Wierichs, Nathan Killoran, Dmitry Grinko, M. Cerezo, Martin Larocca Classical shadows (CS) has recently emerged as an important framework to efficiently predict properties of an unknown quantum state. A common strategy in CS protocols is to parametrize the basis in which one measures the state by a random group action; many examples of this have been proposed and studied on a case-by-case basis. In this work, we present a unified theory that allows us to simultaneously understand CS protocols based on sampling from general group representations, extending previous approaches that worked in simplified (multiplicity-free) settings. We identify a class of measurement bases which we call "centralizing bases" that allows us to analytically characterize and invert the measurement channel, minimizing classical post-processing costs. We complement this analysis by deriving general bounds on the sample-complexity necessary to obtain estimates of a given precision. Beyond its unification of previous CS protocols, our method allows us to readily generate new protocols based on other groups, or different representations of previously considered ones. For example, we characterize novel shadow protocols based on sampling from the spin and tensor representations of \textsf{SU}(2), symmetric and orthogonal groups, and the exceptional Lie group G_2. Comments: 11 + 41 pages, 7 figures Subjects: Quantum Physics (quant-ph) Report number: LA-UR-25-27225 Cite as: arXiv:2604.01429 [quant-ph]   (or arXiv:2604.01429v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.01429 Focus to learn more Submission history From: Maxwell West [view email] [v1] Wed, 1 Apr 2026 22:09:44 UTC (481 KB) Access Paper: HTML (experimental) 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?)