Nearly Heisenberg-limited noise-unbiased frequency estimation by tailored sensor design

We consider entanglement-assisted frequency estimation by Ramsey interferometry, in the presence of dephasing noise from spatiotemporally correlated environments.By working in the widely employed local estimation regime, we show that even for infinite measurement statistics, noise renders standard estimators biased or ill-defined. We introduce ratio estimators which, at the cost of doubling the required resources, are insensitive to noise and retain the asymptotic precision scaling of standard ones. While ratio estimators are applicable also in the limit of Markovian noise, we focus on non-Markovian dephasing from a bosonic bath and show how knowledge about the noise spectrum may be used to maximize metrological advantage, by tailoring the sensor's geometry. Notably, Heisenberg scaling is attained up to a logarithmic prefactor by maximally entangled states.