  Quantum metrology fundamentally relies upon the efficient management of
quantum uncertainties. We show that, under equilibrium conditions, the
management of quantum noise becomes extremely flexible around the quantum
critical point of a quantum many-body system: this is due to the critical
divergence of quantum fluctuations of the order parameter, which, via
Heisenberg's inequalities, may lead to the critical suppression of the
fluctuations in conjugate observables. Taking the quantum Ising model as the
paradigmatic incarnation of quantum phase transitions, we show that it exhibits
quantum critical squeezing of one spin component, providing a scaling for the
precision of interferometric parameter estimation which, in dimensions $d \geq
2$, lies in between the standard quantum limit and the Heisenberg limit.
Quantum critical squeezing saturates the maximum metrological gain allowed by
the quantum Fisher information in $d=\infty$ (or with infinite-range
interactions) at all temperatures, and it approaches closely the bound in a
broad range of temperatures in $d=2$ and 3. This demonstrates the immediate
metrological potential of equilibrium many-body states close to quantum
criticality, which are accessible \emph{e.g.} to atomic quantum simulators via
elementary adiabatic protocols.
