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We consider all pure or mixed states of a quantum many-body system whichexhibit the same, arbitrary but fixed measurement outcome statistics forseveral commuting observables. Taking those states as initial conditions, whichare then propagated by the pertinent Schr\"odinger or von Neumann equation upto some later time point, and invoking a few additional, fairly weak andrealistic assumptions, we show that most of them still entail very similarexpectation values for any given observable. This so-called dynamicaltypicality property thus corroborates the widespread observation that a fewmacroscopic features are sufficient to ensure the reproducibility ofexperimental measurements despite many unknown and uncontrollable microscopicdetails of the system. We also discuss and exemplify the usefulness of ourgeneral analytical result as a powerful numerical tool.

Dynamical typicality for initial states with a preset measurement statistics of several commuting observables