  Uncertainty lower bounds for parameter estimations associated with a unitary
family of mixed-state density matrices are obtained by embedding the space of
density matrices in the Hilbert space of square-root density matrices. In the
Hilbert-space setup the measure of uncertainty is given by the skew information
of the second kind, while the uncertainty lower bound is given by the
Wigner-Yanase skew information associated with the conjugate observable.
Higher-order corrections to the uncertainty lower bound are determined by
higher-order quantum skew moments; expressions for these moments are worked out
in closed form.
