Non-Markovian quantum dynamics: What does it mean?

¹ CAS Key Laboratory of Quantum Information, University of Science and Technology of China Hefei 230026, China
² CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China - Hefei 230026, China
³ Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku FI-20014 Turun yliopisto, Finland

^(a) cfli@ustc.edu.cn
^(b) jyrki.piilo@utu.fi

Received: 27 August 2019
Accepted: 13 September 2019

Abstract

During the last ten years, the studies on non-Markovian open system dynamics has become increasingly popular and having contributions from diverse sets of research communities. This interest has arisen due to fundamental problematics as to how to define and quantify memory effects in the quantum domain, how to exploit and develop applications based on them, and also due to the following question: what are the ultimate limits for controlling open system dynamics? We give here a simple theoretical introduction to the basic approaches to define and quantify quantum non-Markovianity —also highlighting their connections and differences. In addition to the importance of the development for open quantum systems studies, we also discuss the implications of the progress for other fields including, e.g., formal studies of stochastic processes and quantum information science, and conclude with possible future directions the recent developments open.