Witness of non-Markovian dynamics based on Bhattacharyya quantum distance

Non-Markovian effects due to quantum memory in the dynamics of open systems typically correspond to information backflows from the surrounding environment to the system. We propose a witness to quantify the non-Markovianity of quantum evolutions using the Bhattacharyya distance (BD), a specific quantum statistical distance. This witness has the advantage of not requiring the calculation of the evolved density matrix and only computes through the initial and final states of the system, therefore leading to the improvement of quantum metrology. It means that we calculate the quantum angle between two states to detect non-Markovian effects. This proposal is investigated by considering several instances of open quantum systems, such as two and three-level atoms interacting in single and two-mode fields, respectively, and two effective two-level atoms interacting locally with two independent environments. We demonstrate that the suggested BD-based non-Markovianity witness identifies memory effects, consistent with well-established witnesses based on Bures distance, quantum Fisher information, and Hilbert-Schmidt speed, showing sensitivity to information backflows.