Quantum Filtering for Linear Dynamical Quantum Systems

Abstract

This chapter introduces quantum filtering theory as a quantum analogue of stochastic filtering theory. When applied to linear quantum systems, this leads to a quantum version of the Kalman filter. Concepts from quantum probability theory that are relevant to quantum filtering theory are introduced, including a suitable notion of quantum conditional expectations. The chapter also briefly introduces robust observers for linear quantum systems to deal with modeling uncertainties for the purpose of estimation.