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.
[1]
C. Monroe,et al.
Architecture for a large-scale ion-trap quantum computer
,
2002,
Nature.
[2]
W. Itano.
Quadrupole moments and hyperfine constants of metastable states of Ca{sup +}, Sr{sup +}, Ba{sup +}, Yb{sup +}, Hg{sup +}, and Au
,
2005,
physics/0512250.
[3]
J. Cole,et al.
Derivation of Markovian master equations for spatially correlated decoherence
,
2013,
1301.1381.
[4]
S. Braunstein,et al.
Statistical distance and the geometry of quantum states.
,
1994,
Physical review letters.
[5]
J. Cirac,et al.
Improvement of frequency standards with quantum entanglement
,
1997,
quant-ph/9707014.