Adaptive detection of Rabi signals under composite hypotheses

• URL: http://arxiv.org/abs/2609.16119v1
• Date: Mon, 14 Sep 2026 18:00:01 GMT
• Title: Adaptive detection of Rabi signals under composite hypotheses
• Abstract summary: Motivated by searches for weak coherent drives, we formulate repeated quantum sensing with a fixed shot budget.<n>We benchmark detection power, sensitivity, and Type-II error exponents in the resonant case with unknown signal amplitude and phase.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Motivated by searches for weak coherent drives, we formulate repeated quantum sensing with a fixed shot budget as an asymmetric composite hypothesis test. Taking Rabi sensing as a concrete example, we benchmark detection power, sensitivity, and Type-II error exponents in the resonant case with unknown signal amplitude and phase. We compare non-adaptive population and transverse readouts with a myopic Bayesian policy that selects each projective axis by maximizing the expected information gain in one step. The common decision statistic is a log Bayes factor, with a policy specific threshold calibrated under the null to enforce a common Type-I error. A weak signal expansion shows that population readout is phase independent but quadratic in amplitude, giving $n^{-1/4}$ sensitivity, whereas transverse readout is linear in amplitude and permits $n^{-1/2}$ sensitivity without adaptation, but is phase-dependent. In Monte Carlo pseudoexperiments, the adaptive policy exploits posterior information about the unknown direction to guide subsequent readouts; its sensitivity is consistent with $n^{-1/2}$ over the simulated large $n$ range and, at the largest simulated shot counts, outperforms the fixed transverse schedules. Its phase-averaged effective Type-II exponent also exceeds the non-adaptive references over the simulated range. These results demonstrate the finite budget value of exploiting nuisance parameter information under calibrated false positive control.

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