The Zeno limit in frequency estimation with non-Markovian environments

Abstract: We prove the Zeno limit $N^{3/2}$ 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.