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pith:KMRD6DLN

pith:2024:KMRD6DLNZX25UMTAGTSZV3TASD

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Two-stage Quantum Estimation and the Asymptotics of Quantum-enhanced Transmittance Sensing

Boulat A. Bash, Zihao Gong

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.

arxiv:2402.17922 v3 · 2024-02-27 · quant-ph · cs.IT · math.IT · math.ST · stat.TH

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Claims

C1strongest 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.

C2weakest 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. This premise enters in the description of the two-stage approach and its relaxation of prior conditions.

C3one 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.

References

39 extracted · 39 resolved · 1 Pith anchors

[1] On two-stage quantum estimation and asymptotics of quantum-enhanced transmittance sensing, 2024

[2] C. W. Helstrom, Quantum Detection and Estimation Theory. New York, NY , USA: Academic Press, Inc., 1976 1976

[3] An asymptotically efficient estimator for a one- dimensional parametric model of quantum statistical operators, 1988

[4] Strong consistency and asymptotic efficiency for adaptive quantum estimation problems, 2006

[5] State estimation for large ensembles, 2000

Receipt and verification

First computed	2026-06-01T01:02:11.770350Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

53223f0d6dcdf5da326034e59aee6090ce7eb4786ebaeb8b8f8273245e81173e

Aliases

arxiv: 2402.17922 · arxiv_version: 2402.17922v3 · doi: 10.48550/arxiv.2402.17922 · pith_short_12: KMRD6DLNZX25 · pith_short_16: KMRD6DLNZX25UMTA · pith_short_8: KMRD6DLN

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/KMRD6DLNZX25UMTAGTSZV3TASD \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 53223f0d6dcdf5da326034e59aee6090ce7eb4786ebaeb8b8f8273245e81173e

Canonical record JSON

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    "abstract_canon_sha256": "47bea69226a7c6337717b1de6ba903a0f874a9c7aee3dc86c0ea27fa93ebfd7a",
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      "math.ST",
      "stat.TH"
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    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2024-02-27T22:28:42Z",
    "title_canon_sha256": "40822dc5ae9fe2d3205daebacd57d8c150223d765c6b67a63b239840bdf8f856"
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  "source": {
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    "kind": "arxiv",
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