Abstract
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.
Highlights
For closed quantum systems, which are isolated from its surroundings, the dynamic is unitary and different bounds on QSL-time have been obtained based on Bures angle and relative purity as the distance measures between initial and target state [5,6,7,8,9,10,11,12]
By making use of various distance measures, different bounds on the QSL-time have been proposed for open quantum systems [16,17,18,19,20,21,22,23,24,25,26]
It is showed that for damped Jaynes-Cummings model the QSL-time has the inverse relation with quantum coherence in Schwarzschild space-time
Summary
For closed quantum systems, which are isolated from its surroundings, the dynamic is unitary and different bounds on QSL-time have been obtained based on Bures angle and relative purity as the distance measures between initial and target state [5,6,7,8,9,10,11,12]. When τ(QSL) < τD, the potential capacity for further acceleration will be greater Another important point to be noted here is that, when the coupling strength between the system and environment is weak τ(QSL) tends to the actual driving time τD. In this work we will consider the setting in which quantum system freely falls into the Schwarzschild black hole hovers near the event horizon and it interacts with surroundings in the damped Jaynes-Cummings or Ohmic like dephasing models. 3, we discuss about important exclusivity of Dirac fields in Schwarzschild space-time to express the QSL-time for open quantum systems in the background of a black hole.
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