Identifiability of Autonomous and Controlled Open Quantum Systems

TL;DR

This paper explores the identifiability of open quantum systems, linking quantum state reconstruction to classical system identification, and establishes conditions for system and state recoverability.

Contribution

It introduces a unified framework for autonomous and controlled open quantum systems, connecting quantum measurement dynamics with classical identification theory.

Findings

Conditions for quantum state reconstructibility

Analysis of full master equation recovery

Framework for system matrix identification

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. Both of 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.