  We analyze families of measures for the quantum statistical speed which
include as special cases the quantum Fisher information, the trace speed, i.e.,
the quantum statistical speed obtained from the trace distance, and more
general quantifiers obtained from the family of Schatten norms. These measures
quantify the statistical speed under generic quantum evolutions and are
obtained by maximizing classical measures over all possible quantum
measurements. We discuss general properties, optimal measurements, and upper
bounds on the speed of separable states. We further provide a physical
interpretation for the trace speed by linking it to an analog of the quantum
Cram\'{e}r-Rao bound for median-unbiased quantum phase estimation.
