Hierarchy of quantum correlations under non-Markovian dynamics

We investigate the dynamics of quantum correlations (QC) under effects reservoir memory, as a resource for information and computation tasks. Quantum two-qubit systems are used implementing teleportation successfully, investigating how fidelity, violation Bell-CHSH inequality, steering entanglement connected with each other influence noisy environments. Both Markovian non-Markovian channels considered, it is shown that decay revival follow hierarchy in state space. Noise tolerance checked different types unital non-unital channels, without memory. The speed limit time $(\tau_{QSL})$ investigated from perspective memory noise, corresponding to analyze evolution correlations. establish connection between backflow, channels.