Convex resource theory of non-Markovianity

We establish a convex resource theory of non-Markovianity inducing information backflow under the constraint of small time intervals within the temporal evolution. We identify the free operations and a generalized bona-fide measure of non-Markovian information backflow. The framework satisfies the basic properties of a consistent resource theory. The proposed resource quantifier is lower bounded by the optimization free Rivas–Huelga–Plenio (RHP) measure of non-Markovianity. We next define the robustness of non-Markovianity and show that it can directly linked with the RHP measure of non-Markovianity through a lower bound. This enables a physical interpretation of the RHP measure. We further relate robustness of non-Markovianity with the quantum capacity of dephasing channels.