Protection of Entanglement in the presence of Markovian or Non-Markovian Environment via particle velocity : Exact Results

On the analytic ground we examine a physical mechanism how particle velocity can protect an entanglement when quantum system is embedded in Markovian or non-Markovian environment. In particular the effect of particle velocity is examined in the entanglement sudden death (ESD) and revival of entanglement (ROE) phenomena. Even though particles move fast, the ESD phenomenon does not disappear if it occurs at zero velocity. However the time domain $0 \leq t \leq t_*$ for nonvanishing entanglement becomes larger and larger with increasing velocity. When ROE phenomenon occurs at zero velocity, even small velocity can make this phenomenon not to occur although the oscillatory behavior of entanglement in time is maintained. For comparatively large velocity the amplitude of the oscillatory behavior becomes extremely small. In this way the entanglement can be protected by particle velocity. The protection of entanglement via velocity is compared with that via the detuning parameter.