  We elaborate on a Hilbert-Schmidt distance measure assessing the intrinsic
metrological accuracy in the detection of signals imprinted on quantum probe
states by signal-dependent transformations. For small signals this leads to a
probe-transformation measure $\Lambda$ fully symmetric on the probe $\rho$ and
the generator $G$ of the transformation $\Lambda (\rho, G) = \Lambda (G,
\rho)$. Although $\Lambda$ can be regarded as a generalization of variance we
show that no uncertainty relation holds for the product of measures
corresponding to complementary generators. We show that all states with
resolution larger than coherent states are nonclassical. We apply this
formalism to feasible probes and transformations.
