  Quantum systems used for metrology can offer enhanced precision over their
classical counterparts. The design of quantum sensors can be optimized by
maximizing the quantum Fisher information (QFI), which characterizes the
precision of parameter estimation for an ideal measurement. Here we consider
the response of a quantum system as a means to estimate the strength of an
external perturbation that has been switched on slowly. General expressions for
the QFI are derived, which also hold for interacting many-body systems in the
thermodynamic limit at finite temperatures, and can be related to
linear-response transport coefficients. For quantum dot nanoelectronics
devices, we show that electron interactions can lead to exponential scaling of
the QFI with system size, highlighting that quantum resources can be utilized
in the full Fock space. The precision estimation of voltages and fields can
also be achieved by practical global measurements, such as the electric
current, making quantum circuits good candidates for metrological applications.
