Attainable and usable coherence in X states over Markovian and non-Markovian channels

The relations between the resource theoretic measures of quantum coherence are rigorously investigated for various Markovian and non-Markovian channels two-qubit $X$ states with specific attention to maximum minimum attainable usefulness these in performing teleportation noisy environment. investigation has revealed that under both dephasing dissipative type noises maximally entangled mixed Werner lose their form usefulness. However, non-local (MNMSs) identity noise only. Thus, MNMSs established be useful teleporting a qubit fidelity greater than classical limit presence noise. also remain device independent key distribution this case as they still violate Bell's inequality. In noise, measured by relative entropy is found fall faster same using $l_1$ norm coherence. Further, information back-flow from environment system observed over which leads revival Additionally, sequential interaction two qubits result correlated on qubits, frozen channel. Under effect studied here, we have coherence, i.e., amount among feature not visible any state evolving channels.