Quantum filtering and propagation of chaos for open quantum systems, with applications to quantum feedback control and quantum mean-field games

Abstract

The theory of quantum filtering (of quantum continuous measurements) was developed by V.P. Belavkin about 40 years ago. Since then it attracted attention of numerous investigators including mathematicians, theoretical and experimental physicists. However, the rigorous mathematical theory of the filtering equations for mixed states in basic infinite-dimensional quantum systems remained an open problem, which was resolved by the author recently. This survey paper presents in full the mathematical theory of quantum filtering equations, their rigorous derivation from basic principles, the corresponding law of large number limits (propagation of chaos) and related topics. Applications to feedback control, quantum dynamic and mean-field games are discussed.