Efficient measure of information backflow with quasi-stochastic process

Abstract: Characterization and quantification of non-Markovian dynamics in open quantum systems is a topical issue in the rapidly developing field of quantum computation and quantum communication. A standard approach based on the notion of information backflow detects the flow of information from the environment back to the system. Numerous measures of information backflow have been proposed using different definitions of distinguishability between pairs of quantum states. These measures, however, necessitate optimization over the state space which can be analytically challenging or numerically demanding. Here, we propose an alternative witness and measure of information backflow that is explicitly state-independent by utilizing the concept of quasiprobability representation and recent advances in the theory of majorization for quasiprobabilities. We illustrate its use over several paradigmatic examples, demonstrating consistent Markovian conditions with known results and also reported necessary and sufficient condition for qutrit system in random unitary channel. The paper concludes with discussions on the foundational implications of quantum dynamical evolution.