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We analyze families of measures for the quantum statistical speed whichinclude as special cases the quantum Fisher information, the trace speed, i.e.,the quantum statistical speed obtained from the trace distance, and moregeneral quantifiers obtained from the family of Schatten norms. These measuresquantify the statistical speed under generic quantum evolutions and areobtained by maximizing classical measures over all possible quantummeasurements. We discuss general properties, optimal measurements, and upperbounds on the speed of separable states. We further provide a physicalinterpretation for the trace speed by linking it to an analog of the quantumCram\'{e}r-Rao bound for median-unbiased quantum phase estimation.

Statistical speed of quantum states: Generalized quantum Fisher information and Schatten speed