  We study the estimation precision attainable by entanglement-enhanced Ramsey
interferometry in the presence of spatiotemporally correlated non-classical
noise. Our analysis relies on an exact expression of the reduced density matrix
of the qubit probes under general zero-mean Gaussian stationary dephasing,
which is established through cumulant-expansion techniques and may be of
independent interest in the context of non-Markovian open dynamics. By
continuing and expanding our previous work [Beaudoin et al., Phys. Rev. A 98,
020102(R) (2018)], we analyze the effects of a non-collective coupling regime
between the qubit probes and their environment, focusing on two limiting
scenarios where the couplings may take only two or a continuum of possible
values. In the paradigmatic case of spin-boson dephasing noise from a thermal
environment, we find that it is possible to suppress, on average, the effect of
spatial correlations by randomizing the location of the probes, as long as
enough configurations are sampled where noise correlations are negative. As a
result, superclassical precision scaling is asymptotically restored for initial
entangled states, including experimentally accessible one-axis spin-squeezed
states.
