Investigating non-Markovian dynamics of quantum open systems

Mariia Ivanchenko, Peter Walters, Fei Wang

The reduced description of the quantum dynamic processes in the condensed phase environment leads to the equation of motion with a memory kernel. Such a memory effect, termed non-Markovianity, presents more complex dynamics compared to its memoryless or Markovian counterpart, and many chemical systems have been demonstrated through numerical simulations to exhibit non-Markovian quantum dynamics. Explicitly how the memory impacts the dynamic process remains largely unexplored. In this work, we focus on ways to separate the non-Markovian contributions from the dynamics and study the non-Markovian effects. Specifically, we developed a rigorous procedure for mapping the exact non-Markovian quantum propagator to the Lindblad form. Consequently, it allows us to extract the negative decay rate from the Lindbladian that is the signature of the non-Markovianity. By including or excluding the negative rate in the time evolution, we can decisively pinpoint the influence of non-Markovianity on the system's properties such as coherence, entanglement, and equilibrium state distribution. The understanding of such memory effects on the dynamic process suggests the possibility of leveraging non-Markovianity for quantum control.

Carole Addis

Dariusz Chruściński, Andrzej Kossakowski

Charlotte Bäcker, Nick Maryshchak, Walter T. Strunz

A profound understanding of decoherence and dissipation in quantum dynamics is crucial for the realistic modeling of the evolution of quantum systems. In open quantum dynamics one distinguishes between a memoryless, so-called Markovian evolution and dynamics incorporating memory effects, termed non-Markovian. In this work we study how prevalent memory effects are in the set of all such dynamics. We thus investigate how often a Markovian description is applicable. This question is approached by investigating randomly generated two-step qubit dynamics with respect to different concepts and witnesses of non-Markovianity. We observe that almost all dynamics are non-Markovian, and only a small (yet finite) fraction is Markovian. Furthermore, we study how this proportion changes when considering certain subclasses such as lower rank or mixed-unitary dynamics. Importantly, our results shed light on the relative ratios of -- and interrelations between -- the sets of dynamics that are non-Markovian with respect to different criteria. Finally, we investigate the fraction of dynamics in which the memory effects are necessarily of quantum nature and establish a connection between two recently developed concepts that characterize the quantumness of memory in non-Markovian dynamics.

Shunlong Luo, Shuangshuang Fu, Hongting Song

In the study of open quantum systems, memory effects are usually ignored, and this leads to dynamical semigroups and Markovian dynamics. However, in practice, non-Markovian dynamics is the rule rather than the exception. With the recent emergence of quantum information theory, there is a flurry of investigations of non-Markovian dynamics, and several significant measures for non-Markovianity are introduced from various perspectives such as deviation from divisibility, information exchange between a system and its environment, or entanglement with the environment. In this work, by exploiting the correlations flow between a system and an arbitrary ancillary, we propose a considerably intuitive measure for non-Markovianity by use of correlations as quantified by the quantum mutual information rather than entanglement. The fundamental properties, physical significance, and differences and relations with existing measures for non-Markovianity are elucidated. The measure captures quite directly and deeply the characteristics of non-Markovianity from the perspective of information. A simplified version based on Jamio\l{}kowski-Choi isomorphism which encodes operations via bipartite states and does not involve any optimization is also proposed.

Yusui Chen, Ting Yu

In this review we discuss recent progress in the theory of open quantum systems based on non-MarkovianNon-Markovian quantum state diffusionQuantum state diffusion equation and master equationsMaster equation. In particular, we show that an exact master equation for an open quantum system consisting of a few qubits can be explicitly constructed by using the corresponding non-Markovian quantum state diffusion equation. The exact master equation arises naturally from the quantum decoherence dynamics of qubit systems collectively interacting with a colored noise. We illustrate our general theoretical formalism by the explicit construction of a three-qubit system coupled to a non-Markovian bosonic environment. This exact qubit master equation accurately characterizes the time evolution of the qubit system in various parameter domains, and paves the way for investigation of the memory effect of an open quantum system in a non-Markovian regime without any approximation.