We prove the Zeno limit N3/2 of the quantum Fisher information for frequency estimation with a general initial state of N two-level atoms in the presence of local non-Markovian dephasing noise, which was demonstrated for a GHZ state by A. W. Chin, S. F. Huelga, M. B. Plenio (2012). For collective dephasing we prove that non-Markovian noise allows for better scaling for both correlated and uncorelated states. The quantum enhancement in precision is at least as good as in the local case.
@article{arxiv.1403.1333,
title = {The Zeno limit in frequency estimation with non-Markovian environments},
author = {Katarzyna Macieszczak},
journal= {arXiv preprint arXiv:1403.1333},
year = {2014}
}