  The evaluation of the minimal evolution time between two distinguishable
states of a system is important for assessing the maximal speed of quantum
computers and communication channels. Lower bounds for this minimal time have
been proposed for unitary dynamics. Here we show that it is possible to extend
this concept to nonunitary processes, using an attainable lower bound that is
connected to the quantum Fisher information for time estimation. This result is
used to delimit the minimal evolution time for typical noisy channels.
