Information trapping in quantum communications

Many quantum systems display Markovian and non-Markovian behaviors with the information flow and backflow between the system and the surrounding environment. In this paper, we introduce a definition of the dynamics of open quantum systems called information trapping, which is a special case of the information flow. We show that under specific conditions, the information flow can exhibit behavior beyond Markovian or non-Markovian system dynamics. The physical reason behind this phenomenon may arise from the entanglement between the system and the environment, such that the rates of entangling and disentangling can equalize over time, influenced by the quantum memory of the system and environmental decoherence effects. This proposal is investigated by considering some witnesses of the behavior of the system dynamics such as fidelity, trace distance, the Holevo quantity, and Hilbert-Schmidt speed in the quantum teleportation and dense coding protocols based on the open quantum system consisting of an $XXZ$ chain Heisenberg affected by intrinsic decoherence. The main achievement of this work is focused on facilitating access to faithful quantum communication.