Geometric signature of non-Markovian dynamics

Dariusz Chruściński, Andrzej Kossakowski

PAULO SÉRGIO DE ANDRADE

The characterization of non-Markovian dynamics in open quantum systems remains a central challenge in quantum physics. Conventional measures often rely on specific properties of the system's evolution, such as the flow of information or the divisibility of the dynamical map. This paper introduces a fundamentally different approach by connecting quantum memory effects to the topological structure of the system's path space. We posit that the set of all possible quantum trajectories, when viewed as a geometric object, exhibits distinct topological signatures under non-Markovian evolution compared to its Markovian counterpart. Using tools from topological data analysis, specifically persistent homology, we analyze the path space generated from simulations of a canonical open quantum system. We demonstrate that topological invariants, such as the Betti numbers, which count holes and voids in the path space, serve as robust indicators of non-Markovianity. Our results reveal that the presence of quantum memory induces non-trivial topological features, such as persistent loops, in the space of paths. This suggests that memory effects constrain the system's evolution, forcing trajectories to organize into complex, non-contractible structures. This topological framework provides a model-agnostic and potentially more robust method for detecting and quantifying quantum memory, opening new avenues for understanding complex quantum dynamics from a geometric perspective.

Bassano Vacchini

We consider the issue of non-Markovianity of a quantum dynamics starting from a comparison with the classical definition of Markovian processes. We point to the fact that two sufficient but not necessary signatures of non-Markovianity of a classical process find their natural quantum counterpart in recently introduced measures of quantum non-Markovianity. This behaviour is analysed in detail for quantum dynamics which can be built taking as input a class of classical processes.

Dariusz Chruściński

Chikako Uchiyama

Arapat Ablimit, Dildar Hitjan, Ahmad Abliz

Abstract In this paper, we study the geometric quantum discord dynamics of the double quantum dot charge qubit in the non-Markovian environment. We apply the non-perturbative non-Markovian quantum state diffusion method to obtain the exact master equation of the double quantum dot system coupled to two independent non-zero temperature electronic baths. Then, we use this master equation to investigate the effects of non-Markovianity, inter-dot coupling strength and bath temperature on the dynamics of geometric quantum discord. Our studies show that the geometric quantum discord of a double quantum dot system can be modified and enhanced in some cases via these factors.