Rivas, ÁngelLuis Aina, Alfredo2023-06-202023-06-202008-06-101050-294710.1103/PhysRevA.77.063813https://hdl.handle.net/20.500.14352/51486©2008 The American Physical Society. A.R. acknowledges financial support from the University of Hertfordshire and the EU Integrated Project QAP. A.L. acknowledges support from the Universidad Complutense Project No. PR1-A/07-15378.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 Λ(ρ,G)= Λ(G,ρ). Although Λ 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.engjournal articlehttp://dx.doi.org/10.1103/PhysRevA.77.063813http://journals.aps.org/open access535Hilbert-schmidt distanceQuantum statesEntanglement measuresProjection noiseClassicalityLimitÓptica (Física)2209.19 Óptica Física