  We quantify the impact of spatio-temporally correlated Gaussian quantum noise
on frequency estimation by Ramsey interferometry. While correlations in a
classical noise environment can be exploited to reduce uncertainty relative to
the uncorrelated case, we show that quantum noise environments with frequency
asymmetric spectra generally introduce additional sources of uncertainty due to
uncontrolled entanglement of the sensing system mediated by the bath. For the
representative case of collective noise from bosonic sources, and
experimentally relevant collective spin observables, we find that the
uncertainty can increase exponentially with the number of probes. As a concrete
application, we show that correlated quantum noise due to a lattice vibrational
mode can preclude superclassical precision scaling in current amplitude sensing
experiments with trapped ions.
