{"paper":{"title":"Two-stage Quantum Estimation and the Asymptotics of Quantum-enhanced Transmittance Sensing","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A relaxed two-stage quantum estimation method broadens the class of usable preliminary estimators while achieving near-QCRB asymptotics for single-parameter problems including transmittance sensing.","cross_cats":["cs.IT","math.IT","math.ST","stat.TH"],"primary_cat":"quant-ph","authors_text":"Boulat A. Bash, Zihao Gong","submitted_at":"2024-02-27T22:28:42Z","abstract_excerpt":"We consider estimation of a single unknown parameter embedded in a quantum state. Quantum Cram\\'er-Rao bound (QCRB) is the ultimate limit of the mean squared error for any unbiased estimator. While it can be achieved asymptotically for a large number of quantum state copies, the measurement required often depends on the true value of the parameter of interest. Prior work addresses this paradox using a two-stage approach: in the first stage, a preliminary estimate is obtained by applying, on a vanishing fraction of quantum state copies, a sub-optimal measurement that does not depend on the para"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We relax these conditions to substantially broaden the class of usable estimators for single-parameter problems at the cost of slightly weakening the asymptotic properties of the two-stage method. We also account for nuisance parameters. We apply our results to obtain the asymptotics of quantum-enhanced transmittance sensing.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that a preliminary estimate obtained from a vanishing fraction of copies using a parameter-independent measurement is sufficient to construct the QCRB-achieving measurement for the remaining copies while preserving the (slightly weakened) asymptotic properties. This premise enters in the description of the two-stage approach and its relaxation of prior conditions.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Relaxes conditions on two-stage quantum estimators to broaden usable classical post-processing while deriving asymptotics for quantum-enhanced transmittance sensing with nuisance parameters.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A relaxed two-stage quantum estimation method broadens the class of usable preliminary estimators while achieving near-QCRB asymptotics for single-parameter problems including transmittance sensing.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"e4fa49502d3c6fa3f606a100634236564584b26560e5f2f13a20a9a6e1470561"},"source":{"id":"2402.17922","kind":"arxiv","version":3},"verdict":{"id":"b58538b5-7342-4c59-84f7-302d88e1b306","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-24T03:35:15.468481Z","strongest_claim":"We relax these conditions to substantially broaden the class of usable estimators for single-parameter problems at the cost of slightly weakening the asymptotic properties of the two-stage method. We also account for nuisance parameters. We apply our results to obtain the asymptotics of quantum-enhanced transmittance sensing.","one_line_summary":"Relaxes conditions on two-stage quantum estimators to broaden usable classical post-processing while deriving asymptotics for quantum-enhanced transmittance sensing with nuisance parameters.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that a preliminary estimate obtained from a vanishing fraction of copies using a parameter-independent measurement is sufficient to construct the QCRB-achieving measurement for the remaining copies while preserving the (slightly weakened) asymptotic properties. 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