Single-shot measurement learning as a self-certifying estimator for quantum-enhanced sensing

Abstract

Single-shot measurement learning (SSML) learns a compensation unitary from a one-bit success/failure record and halts after a prescribed run of consecutive successes. We recast SSML as an adaptive estimator on a parameterized sensing manifold and ask what role it can play in quantum-enhanced sensing. First, we show that the terminal run itself furnishes an intrinsic certificate of local alignment: longer terminal runs certify smaller infidelity, and near the optimum this becomes a Fisher-calibrated certificate of parameter error. Second, for compensation-type sensing families, the Bernoulli success/failure record is locally matched to the probe quantum Fisher information (QFI), so SSML preserves the probe's metrological content despite using only one classical bit per copy. In this sense, SSML makes the quantum enhancement carried by the probe operationally available in an online self-terminating protocol. Applied to GHZ/NOON probes of depth $m$, SSML retains the familiar square-root entanglement gain over product probes at fixed total resource, while an ideal multiscale architecture remains compatible with Heisenberg scaling. Monte Carlo simulations of photonic NOON-state phase sensing show the expected near-inverse decay of terminal infidelity with entangled shots, SQL-like total-resource scaling at fixed entanglement depth, the corresponding fixed-resource entanglement gain, the global limitation of a single fringe scale, and the recovery of Heisenberg-compatible behavior under ideal multiscale hand-off. These results identify SSML as a Fisher-preserving, self-certifying estimator layer for quantum-enhanced sensing.