  We consider bipartite systems as versatile probes for the estimation of
transformations acting locally on one of the subsystems. We investigate what
resources are required for the probes to offer a guaranteed level of
metrological performance, when the latter is averaged over specific sets of
local transformations. We quantify such a performance via the average skew
information, a convex quantity which we compute in closed form for bipartite
states of arbitrary dimensions, and which is shown to be strongly dependent on
the degree of local purity of the probes. Our analysis contrasts and
complements the recent series of studies focused on the minimum, rather than
the average, performance of bipartite probes in local estimation tasks, which
was instead determined by quantum correlations other than entanglement. We
provide explicit prescriptions to characterize the most reliable states
maximizing the average skew information, and elucidate the role of state
purity, separability and correlations in the classification of optimal probes.
Our results can help in the identification of useful resources for sensing,
estimation and discrimination applications when complete knowledge of the
interaction mechanism realizing the local transformation is unavailable, and
access to pure entangled probes is technologically limited.
