title: Constructive Method for Detecting the Information Backflow of Non-Markovian Dynamics.
abstract: We investigate the relation between two approaches to the characterization of quantum Markovianity, divisibility and lack of information backflow. We show that a bijective dynamical map is completely positive divisible if and only if a monotonic nonincrease of distinguishability is observed for two equiprobable states of the evolving system and an ancilla. Moreover, our proof is constructive: given any such map that is not completely positive divisible, we give an explicit construction of two states that, when taken with the same a priori probability, exhibit information backflow. Finally, while an ancilla is necessary for the equivalence to hold in general, we show that it is always possible to witness the non-Markovianity of bijective maps without using any entanglement between the system and ancilla.
authors.affiliation: ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain.|Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziądzka 5/7, 87-100 Toruń, Poland.
authors.forename: Bogna
authors.initials: B
authors.lastname: Bylicka
authors.affiliation: ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain.
authors.forename: Markus
authors.initials: M
authors.lastname: Johansson
authors.affiliation: ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain.|ICREA-Institucio Catalana de Recerca i Estudis Avançats, Lluis Companys 23, 08010 Barcelona, Spain.
authors.forename: Antonio
authors.initials: A
authors.lastname: Acín