Identifiability of Autonomous and Controlled Open Quantum Systems
arXiv:2501.05270
The paper studies how to determine (identify) the dynamics of autonomous and controlled open quantum systems by linking their master equations to classical linear and bilinear system identification methods, providing conditions for reconstructing quantum states and system parameters.
Abstract
Open quantum systems are a rich area of research in the intersection of quantum mechanics and stochastic analysis. By considering a variety of master equations, we unify multiple views of autonomous and controlled open quantum systems and, through considering their measurement dynamics, connect them to classical linear and bilinear system identification theory. This allows us to formulate corresponding notions of quantum state identifiability for these systems which, in particular, applies to quantum state tomography, providing conditions under which the probed quantum system is reconstructible. Interestingly, the dynamical representation of the system lends itself to considering two types of identifiability: the full master equation recovery and the recovery of the corresponding system matrices of the linear and bilinear systems. These concepts are discussed in detail, and conditions under which reconstruction is possible are given. We set the groundwork for a number of constructive approaches to the identification of open quantum systems.
14 pages