  Environmental noise can hinder the metrological capabilities of entangled
states. While the use of entanglement allows for Heisenberg-limited resolution,
the largest permitted by quantum mechanics, deviations from strictly unitary
dynamics quickly restore the standard scaling dictated by the central limit
theorem. Product and maximally entangled states become asymptotically
equivalent when the noisy evolution is both local and strictly Markovian.
However, temporal correlations in the noise have been shown to lift this
equivalence while fully (spatially) correlated noise allows for the
identification of decoherence free subspaces. Here we analyze precision limits
in the presence of noise with finite correlation length and show that there
exist robust entangled state preparations which display persistent Heisenberg
scaling despite the environmental decoherence, even for small correlation
length. Our results emphasize the relevance of noise correlations in the study
of quantum advantage and could be relevant beyond metrological applications.
