A Realistic Framework for Quantum Sensing under Finite Resources

Abstract

Quantum-enhanced sensing is commonly benchmarked using the quantum Fisher information (QFI), often interpreted as a direct indicator of achievable precision. However, this quantity acquires operational meaning only within a fully specified inference framework that consistently incorporates state preparation, measurement design, resource accounting, estimator construction, prior information, and finite data effects. Here we establish a realistic end-to-end framework for quantum sensing under finite resources and identify general principles required for operationally meaningful performance assessment. A central conceptual point is that the relevant unit of estimation is not a single detection event but the inference data set required to construct a consistent estimator. We apply this approach to several paradigmatic sensing strategies frequently cited in the literature. Revisiting phase estimation with NOON states within a Bayesian framework under equal total photon resources, we explicitly construct optimal estimators and show that such schemes offer no performance advantage over repeated classical interferometry for global phase estimation with finite prior width. The apparent Heisenberg-like scaling arises predominantly from prior constraints rather than from information gained in the measurement, which is operationally negligible in the resource-normalized sense considered here. We further analyse Holland-Burnett interferometry and homodyne detection with squeezed states, demonstrating how estimator construction and repetition number determine the attainable precision and when QFI provides a reliable diagnostic. Our results clarify the conditions under which nonclassical resources lead to genuine metrological advantages and provide a practical methodology for designing and evaluating quantum sensing protocols under realistic experimental constraints.