Information backflow may not indicate quantum memory

Abstract

We analyze recent approaches to quantum Markovianity and how they relate to the proper definition of quantum memory. We show that the well-known criterion of information backflow does not report a distinction between the quantum or classical character of observed memory effects. Therefore, as a complement to the current description, we propose a definition of a quantum backflow based on the concept of component dynamical maps and convexity arguments. In particular, for a natural choice of component maps, we provide a practical characterization of quantum memory in terms of the new concept of quantum memory witness. In particular, we give a full description of such witnesses in a qubit case. Finally, we discuss a potential generalization of component maps that should capture certain classical features of information backflow.