Quantum Fisher information and flux estimation for localized quantum walks

Determine whether connections analogous to those between Leggett–Garg violations and quantum Fisher information in stationary settings hold for the nonstationary localized preparation used in chiral continuous-time quantum walks and for the estimation of gauge-invariant fluxes.

Background

The paper studies sequential return measurements of a walker initially localized at the measured vertex in a chiral continuous-time quantum walk. Its exact results relate local return amplitudes, measurement back-action, and Leggett–Garg correlations to gauge-invariant fluxes and rooted spectral structure.

The authors note that prior work has connected Leggett–Garg violations to quantum Fisher information in stationary settings, but leave unresolved whether an analogous relationship persists for the nonstationary localized preparation considered here and for flux estimation. Establishing such a connection could clarify the metrological significance of the temporal correlations and help assess the usefulness of local sequential measurements for inferring synthetic gauge fields.