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The paper proposes a way to extract classical Fisher-information bounds, including finite-sample confidence bounds, from standard Bell and CHSH correlation data, without full state tomography. Its most useful point for quantum readers is the tradeoff it identifies: the point of maximal CHSH violation does not necessarily maximize metrological information, so the Bell score is not a drop-in proxy for sensitivity. Results are theoretical, and practical value depends on how well the bounds hold under the real imperfections the authors model, such as visibility loss, accidental coincidences, and multipair emission.
Fisher-Information Certification from Bell Statistics: CHSH Bounds, Information Loss, and Finite-Data Guarantees
arXiv:2610.16702v1 Announce Type: new Abstract: Bell-test data are typically used to certify nonlocal correlations, while quantum metrology is concerned with the sensitivity of measurement statistics to unknown parameters. Here we connect these tasks at the level of experimentally accessible Bell statistics. Using standard moment-based Fisher-information inequalities, we derive lower bounds on the classical Fisher information directly from Bell scores and their parameter dependence, without requiring full state tomography. For CHSH measurements we establish a hierarchy between the information contained in the full outcome record, the set of individual correlators, and the compressed Bell parameter, thereby quantifying the metrological cost of data compression. In polarization-phase sensing, this hierarchy reveals a Bell-metrology tradeoff: the point of maximal CHSH violation need not maximize, and can even suppress, the Fisher information carried by the Bell score itself. We further derive finite-sample lower-confidence bounds from coincidence counts and analyze the effects of biased marginals, accidental coincidences, visibility loss, and multipair emission. The framework provides a practical route for extracting metrological guarantees from Bell-type experiments using only standard correlation measurements.
Abstract:Bell-test data are typically used to certify nonlocal correlations, while quantum metrology is concerned with the sensitivity of measurement statistics to unknown parameters. Here we connect these tasks at the level of experimentally accessible Bell statistics. Using standard moment-based Fisher-information inequalities, we derive lower bounds on the classical Fisher information directly from Bell scores and their parameter dependence, without requiring full state tomography. For CHSH measurements we establish a hierarchy between the information contained in the full outcome record, the set of individual correlators, and the compressed Bell parameter, thereby quantifying the metrological cost of data compression. In polarization-phase sensing, this hierarchy reveals a Bell-metrology tradeoff: the point of maximal CHSH violation need not maximize, and can even suppress, the Fisher information carried by the Bell score itself. We further derive finite-sample lower-confidence bounds from coincidence counts and analyze the effects of biased marginals, accidental coincidences, visibility loss, and multipair emission. The framework provides a practical route for extracting metrological guarantees from Bell-type experiments using only standard correlation measurements.
arXiv:2610.16702 [quant-ph]
(or arXiv:2610.16702v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2610.16702 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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