CHARACTERIZING GENUINE QUANTUM NON-MARKOVIANITY IN STATES AND DYNAMICS

Abstract

Quantum non-Markovianity correlations in state and dynamics are essential to a better understanding of quantum infor mation processing. In this thesis, I have investigated the concept of quantum non-Markovianity in tripartite quantum states, specifically focusing on the distinction between classical and quantum contributions to quantum non-Markovianity. I have proposed a new measure called squashed quantum non-Markovianity (sQNM) to characterize the quantum contributions of non-Markovianity. This measure is based on the quantum conditional mutual information and captures the genuine quantum as pects of non-Markovianity by squashing out all non-quantum contributions of non-Markovianity. I have also shown that sQNM satisfies desirable properties, such as monogamy, asymptotic continuity, convexity, additivity on tensor-product states, general super-additivity, and faithfulness. sQNM is lower bounded by the squashed entanglement between non-conditioning systems and is delimited by the extendibility of either of the non-conditioning systems. Furthermore, I developed a resource theory for genuine quantum non-Markovianity, where free states are identified as those with vanishing sQNM, and free operations are those that do not increase genuine quantum non-Markovianity in states. Notably, I demonstrate an interesting bound on state trans formation under free operations, and the quantum communication costs are closely linked to the sQNM. Additionally, I have shown that it has operational significance, as it determines the optimal rate of private quantum communication in the conditional quantum one-time pad and the minimum deconstruction cost in quantum state deconstruction processes as two times of sQNM. In a parallel investigation, I examine the phenomenon of information revivals in non-Markovian quantum dynamical processes and argue that the notions of information revivals and information backflows, where information flows from the environment back into the system, are distinct. Through detailed analysis, I have demonstrated that information revivals can occur without actual backflow (non-genuine information backflow). I relate these non-causal revivals, the revivals that can be explained without genuine information backflow, to the theory of short Markov chains and squashed quantum non-Markovianity and show that focusing exclusively on processes with genuine information backflow resolves the issue of non-convexity in the study of Markovianity in dynamics. This distinction enables us to construct a convex resource theory for genuine quantum non-Markovianity in dynamics, further advancing the understanding of quantum non-Markovianity and information flow.