Spin squeezing currently constitutes the most reliable method to generate scalable multiparticle entanglement in state-of-the-art atomic interferometers. In principle, the use of squeezed input states can improve the precision in quantum parameter estimation tasks beyond what is achievable by any classical preparation. However, technical noise sources are pervasive in realistic settings and may spoil this advantage. Phase damping, in particular—which includes pure dephasing in the parallel limit—is a leading source of decoherence in present experimental platforms. Quantifying its impact on precision measurements and devising effective strategies to mitigate its deleterious effects therefore remain highly relevant tasks on both fundamental and practical grounds.

In this talk, we consider frequency-estimation protocols that employ squeezed spin states as probes subject to collective phase damping. We show that when the signal and noise quantization axes are not fully aligned, Heisenberg-limited performance can still be achieved, regardless of the temporal correlations of the noise. Furthermore, we prove that the proposed sensing strategy is asymptotically optimal and can be saturated through an appropriate choice of input-state parameters and measurement schemes that are readily accessible in current atomic-interferometry platforms. 

On the other hand, we show that the optimal noiseless strategy, which involves a pre measurement echo, remains best possible when the noise is fully paralell. While a quantum advantage may still be retained in the presence of certain temporally correlated fluctuations, in the relevant limits of Markovian and collored noise with a finite range spectrum, no superclassical scaling of precision can be achieved. Finally, we discuss how augmenting the sensors capabilities by allowing for control in the shape of instantaneous rotations does not lift the above no-go.