An Exponential Advantage for Adaptive Tomography of Structured States under Pauli Basis Measurements
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Quantum Physics arXiv:2604.26043 (quant-ph) [Submitted on 28 Apr 2026] Title:An Exponential Advantage for Adaptive Tomography of Structured States under Pauli Basis Measurements Authors:Alireza Goldar, Zhen Qin, Zhihui Zhu, Zhe-Xuan Gong, Michael B. Wakin View a PDF of the paper titled An Exponential Advantage for Adaptive Tomography of Structured States under Pauli Basis Measurements, by Alireza Goldar and 4 other authors View PDF HTML (experimental) Abstract:Broad claims about whether adaptivity helps in quantum state tomography can be misleading unless the state family, measurement architecture, and error metric are specified carefully. We study a restricted but physically important regime: single-copy quantum state tomography under local Pauli basis measurements, where the allowed measurement settings are tensor-product measurement operators built from local single-qubit Pauli operators, and performance is measured in trace distance with high probability in a minimax sense over a known structured family. We construct an explicit discrete prefix/tree family of states for which adaptive measurement selection achieves polynomial copy complexity, while every non-adaptive design requires exponentially many copies in the worst case. The adaptive upper bound comes from stagewise prefix recovery using hierarchical breadcrumb information revealed by partial prefix matches. The non-adaptive lower bound is based on a rare-prefix mechanism: every fixed design under-samples some deep prefix subset, and outside that subset the competing hypotheses induce identical one-shot laws, so only an exponentially small fraction of the measurement budget contributes to the KL divergence between the full data distributions. The result isolates a concrete regime in which adaptivity provably changes the sample-complexity scaling under the experimentally common local Pauli measurement architecture. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.26043 [quant-ph] (or arXiv:2604.26043v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.26043 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Alireza Goldar [view email] [v1] Tue, 28 Apr 2026 18:26:47 UTC (190 KB) Full-text links: Access Paper: View a PDF of the paper titled An Exponential Advantage for Adaptive Tomography of Structured States under Pauli Basis Measurements, by Alireza Goldar and 4 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 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?)