Enhanced quantum parameter estimation based on the Hardy paradox
Phys. Rev. A 114, 042223 – Published 29 October, 2026
DOI: https://doi.org/10.1103/9t23-rmhv
Abstract
Statistical paradoxes such as the Hardy paradox and the enhancement of phase estimation via postselection both draw upon the same nonclassical features of quantum statistics described by nonpositive quasiprobabilities. In this paper, we introduce a postselected quantum metrology scenario where the initial state, the dynamics associated with the phase shift, and the postselection are all inspired by the Hardy paradox. Specifically, we identify an anomalous weak value that is characteristic of both the Hardy paradox and the potential enhancement of sensitivity by the postselection. We find that the efficiency of the enhancement is reduced when the expectation value associated with the anomalous weak value is different from the inverse of this value. We conclude that the relation between enhanced phase estimation and the Hardy paradox requires a detailed understanding of the relation between weak values and expectation values.
