Quantum metrology in correlated environments

We analytically obtain the precision bounds of frequency measurements in correlated Markovian and non-Markovian environments using a variational approach. The metrological equivalence of product states and maximally entangled states persisting in maximally correlated Markovian and non-Markovian environments is verified using a standard Ramsey spectroscopy setup. Furthermore, we find that optimal measurements can be used to achieve a much higher resolution than standard Ramsey spectroscopy in correlated environments.