Theory of Open Quantum Systems

Heinz‐Peter Breuer, Francesco Petruccione

Fangfang Meng, Shuang Cong

Abstract State transition control of open quantum systems is a research hotspot and difficulty. The control method in the light of the Lyapunov stability theory is a common method. Current research shows that if the open quantum systems meet the constraints that the free Hamiltonian is strong regular and the interaction Hamiltonian is fully connected, by devising appropriate control fields in the light of the Lyapunov stability theory, the open quantum system can move to the desired final state. In view of the fact that most practical open quantum systems do not meet these two constraints, this paper propose a control method. The implicit function perturbation terms are introduced into the control fields to resolve the problem that the open quantum systems do not meet these two convergence constraints. And the main control fields are devised in the light of the Lyapunov stability theory to make the state transition of the open quantum systems converging to the desired final state.

Ohad Shpielberg

The macroscopic fluctuation theory provides a complete hydrodynamic description of nonequilibrium classical diffusive systems. As a first step towards a diffusive theory of open quantum systems, we propose a microscopic open quantum system model —the selective dephasing model. It exhibits genuine quantum diffusive scaling. Namely, the dynamics is diffusive and the density matrix remains entangled at large length scales and long time scales.

E. B. Davies

M. R. James, John Edward Gough

The purpose of this paper is to extend J.C. Willems' theory of dissipative systems to open quantum systems described by quantum noise models. This theory, which combines ideas from quantum physics and control theory, provides useful methods for analysis and design of dissipative quantum systems. We describe the interaction of the plant and a class of external systems, called exosystems, in terms of feedback networks of interconnected open quantum systems. Our results include an infinitesimal characterization of the dissipation property, which generalizes the well-known Positive Real and Bounded Real Lemmas, and is used to study some properties of quantum dissipative systems. We also show how to formulate control design problems using network models for open quantum systems, which implements Willems' “control by interconnection” for open quantum systems. This control design formulation includes, for example, standard problems of stabilization, regulation, and robust control.