Discrete dynamics and non-Markovianity

We study discrete quantum dynamics where single evolution step consists of unitary system transformation followed by decoherence via coupling to an environment. Often non-Markovian memory effects are attributed to structured environments whereas here we take a more general approach within discrete setting. In addition of controlling the structure of the environment, we are interested in how local unitaries on the open system allow the appearance and control of memory effects. Our first simple qubit model, where local unitary is followed by dephasing, illustrates how memory effects arise despite of having no-structure in the environment the system is coupled with. We then elaborate this observation by constructing a model for open quantum walk where the unitary coin and transfer operation is augmented with dephasing of the coin. The results demonstrate that in the limit of strong dephasing within each evolution step, the combined coin-position open system always displays memory effects and their quantity is independent of the structure of the environment. Our construction makes possible an experimentally realizable open quantum walk with photons exhibiting non-Markovian features.