Non-Markovianity and Information Flow

Open quantum systems can be broadly classified into two different categories, Markovian and non-Markovian. Traditionally, Markovian open quantum systems have been described by master equations in the so called Lindblad form. Non-Markovian master equations, on the contrary, have been broadly classified as those types of master equations that cannot be recast in Lindblad form.



Very recently Non-Markovian open quantum systems have attracted a lot of attention for at least three reasons. The first one is the incredible technological advances in the coherent control of systems, such as Josephson junctions, atom lasers, photonic crystals, quantum dots, and even (quantum) biological systems, which cannot be described by Markovian master equations. The second reason is the increasing interest in reservoir engineering, allowing for example to modify the spectral properties of the environment inducing a non-Markovian dynamics. The third reason is of more fundamental nature: Markovian master equations are always the result of approximations and a non-Markovian description is required to describe, e.g., phenomena like the Quantum Zeno effect.



In my talk I will review very recent developments in the non-Markovian theory of open quantum systems focussing on current fundamental questions in this field. Finally I will briefly discuss two examples in which the non-Markovianity measure, quantifying information flow between the system and the environment, is used in the context of both impurities in ultracold atomic gases and generic continuous variable systems.