In this talk, we will discuss a recently introduced measure of genuine quantum non-Markovianity called squashed quantum non-Markovianity (sQNM). It is based on quantum conditional mutual information and quantifies non-Markovinaity after squashing out all possible non-genuine
quantum non-Markovian correlations. This measure is in a similar spirit of squashed entanglement, a faithful entanglement monotone. The genuine quantum non-Markovianity can also be quantified in terms of generalized divergence of recovery. With these in hand, we are able to formulate a resource-theoretic framework to characterize genuine quantum non-Markovianity in quantum states as a resource and discuss its role or connection in some of the operational quantum information processing tasks.
Reference: https://arxiv.org/abs/2311.18323