Quantifying non-Markovianity via local quantum Fisher information

Characterizing non-Markovianity in open quantum systems (OQSs) is gaining increasing attention due to its profound implications for quantum information processing. This phenomenon arises from the system’s evolution being influenced by its previous interactions with the environment. To better understand these complex dynamics, various measures have been proposed, including those based on divisibility, quantum mutual information, and trace distance. Each of these measures provides a different perspective on the behavior of OQSs. Here, we introduce a novel approach to quantifying non-Markovianity by focusing on metrological non-classical correlations. This approach is based on a discord-like measure of quantum correlations for multi-component quantum systems known as local quantum Fisher information (LQFI), which was introduced in Kim et al. (2018). It is defined as the minimization of quantum Fisher information with respect to local observables and measurements. Thereby, we examine some examples to clarify the use of our metric by applying it to three different channels: the phase damping channel, the amplitude damping channel, and the depolarizing channel. In contrast to other approaches, this new metric focuses on correlated bipartite $2\otimes d$ systems, has a clear physical interpretation, and effectively captures the features of non-Markovianity. We demonstrate that the non-Markovian or Markovian evolution of an open correlated bipartite system corresponds to an increase or decrease, respectively, in the quantumness of the quantum state. This quantumness is quantified by the maximum of the measurement-induced Fisher information across all local von Neumann measurements. Compared to measuring non-Markovianity based on local quantum uncertainty – a measure of non-classical correlation of the discord type based on single observables – our results confirm that the nonmonotonic evolution of the LQFI reveals a higher degree of backflow of quantum information and is more robust than the corresponding measure based on quantum uncertainty.