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We review the most recent developments in the theory of open quantum systems focusing on situations in which the reservoir memory effects, due to long-lasting and non-negligible correlations between system and environment, play a crucial role. These systems are often referred to as non-Markovian systems. After a brief summary of different measures of non-Markovianity that have been introduced over the last few years we restrict our analysis to the investigation of information flow between system and environment. Within this framework we introduce an important application of non-Markovianity, namely its use as a quantum probe of complex quantum systems. To illustrate this point we consider quantum probes of ultracold gases, spin chains, and trapped ion crystals and show how properties of these systems can be extracted by means of non-Markovianity measures.
We present a detailed investigation of the dynamics of two physically different qubit models, dephasing under the effect of an ultracold atomic gas in a Bose-Einstein condensed (BEC) state. We study the robustness of each qubit probe against environm
The rapidly developing quantum technologies have put forward a requirement to precisely control and measure temperature of microscopic matters at quantum level. Many quantum thermometry schemes have been proposed. However, precisely measuring low tem
Characterisation protocols have so far played a central role in the development of noisy intermediate-scale quantum (NISQ) computers capable of impressive quantum feats. This trajectory is expected to continue in building the next generation of devic
Non-Markovian quantum effects are typically observed in systems interacting with structured reservoirs. Discrete-time quantum walks are prime example of such systems in which, quantum memory arises due to the controlled interaction between the coin a
Machine learning methods have proved to be useful for the recognition of patterns in statistical data. The measurement outcomes are intrinsically random in quantum physics, however, they do have a pattern when the measurements are performed successiv