  Quantum theory sets the bound on the minimal evolution time between initial
and final states of the quantum system. This minimal evolution time can be used
to specify the maximal speed of the evolution in open and closed quantum
systems. Quantum speed limit is one of the interesting issue in the theory of
open quantum systems. One may investigate the influence of the relativistic
effect on the quantum speed limit time. When several observers are placed in
different inertial or non-inertial frames, or in Schwarzschild space-time, the
relativistic effect should be taken into account. In this work, the quantum
speed limit time in Schwarzschild space-time will be studied for two various
model consist of damped Jaynes-Cummings and Ohmic-like dephasing. First, it
will be observed that how quantum coherence is affected by Hawking radiation.
According to the dependence of quantum speed limit time on quantum coherence
and the dependence of quantum coherence on relative distance of quantum system
to event horizon $R_{0}$, it will be represented that the quantum speed limit
time in Schwarzschild space-time is decreased by increasing $R_{0}$ for damped
Jaynes-Cummings model and conversely, It is increased by increasing $R_{0}$ for
Ohmic-like dephasing model .

Quantum Physics;General Relativity and Quantum Cosmology