  The laws of quantum physics place a limit on the speed of computation. In
particular, the evolution time of a system from an initial state to a final
state cannot be arbitrarily short. Bounds on the speed of evolution for unitary
dynamics have long been studied. A few bounds on the speed of evolution for
noisy dynamics have also been obtained recently, which, however, are in general
not tight. In this paper, we present a new framework for quantum speed limit
concerning noisy dynamics. Within this framework we obtain the exact maximal
rotation angle that noisy dynamics can achieve at any given time, which gives
rise to a tight bound on the evolution time for noisy dynamics. The obtained
bound clearly reveals that noisy dynamics are essentially different from
unitary dynamics. Furthermore, we show that the orthogonalization time, which
is the minimum time needed to evolve any state to its orthogonal state, is in
general not applicable to noisy dynamics.
