{"paper":{"title":"Pauli Measurements Are Near-Optimal for Single-Qubit Tomography","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Abhilash Dharmavarapu, Jayadev Acharya, Nengkun Yu, Yuhan Liu","submitted_at":"2025-07-29T16:50:19Z","abstract_excerpt":"We provide the first non-trivial lower bounds for single-qubit tomography algorithms and show that at least ${\\Omega}\\left(\\frac{10^N}{\\sqrt{N} \\varepsilon^2}\\right)$ copies are required to learn an $N$-qubit state $\\rho\\in\\mathbb{C}^{d\\times d},d=2^N$ to within $\\varepsilon$ trace distance. Pauli measurements, the most commonly used single-qubit measurement scheme, have recently been shown to require at most $O\\left(\\frac{10^N}{\\varepsilon^2}\\right)$ copies for this problem. Combining these results, we nearly settle the long-standing question of the complexity of single-qubit tomography."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.22001","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.22001/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}