Parameter estimation and system identification for continuously-observed quantum systems

Abstract

This paper gives an overview of parameter estimation and system identification for quantum input-output systems by continuous observation of the output field. We present recent results on the quantum Fisher information of the output with respect to unknown dynamical parameters. We discuss the structure of continuous-time measurements as solutions of the quantum Zakai equation, and their relationship to parameter estimation methods. Proceeding beyond parameter estimation, the paper also gives an overview of the emerging topic of quantum system identification for black-box modeling of quantum systems by continuous observation of a traveling wave probe, for the case of ergodic quantum input-output systems and linear quantum systems. Empirical methods for such black-box modeling are also discussed.

arXiv comment25 pages, to appear in Annual Reviews in Control

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• Continuous sensing and parameter estimation with the boundary time-crystal
• Interplay between time and energy in bosonic noisy quantum metrology
• Precision bounds for multiple currents in open quantum systems
• A tensor network approach to sensing quantum light-matter interactions
• Exploiting nonequilibrium phase transitions and strong symmetries for continuous measurement of collective observables
• Parameter estimation for quantum jump unraveling
• Saturability of the Quantum Cramér-Rao Bound in Multiparameter Quantum Estimation at the Single-Copy Level