MEASUREMENT, FILTERING AND CONTROL IN QUANTUM OPEN DYNAMICAL SYSTEMS

A Markovian model for a quantum automata, i.e. an open quantum dynamical system with input and output channels and a feedback is described. A multi-stage version of the theory of quantum measurement and statistical decisions applied to the optimal control problem for quantum dynamical discrete-time objects is developed. Quantum analogies of Stratonovich nonstationary filtering and Bellman quantum dynamical programming for the discrete time are obtained. The Gaussian case of quantum one-dimensional linear Markovian dynamical system with a quantum linear transmission line is studied. The optimal quantum multi-stage decision rule consisting of the classical linear optimal control strategy and quantum optimal filtering procedure is found. The latter contains the optimal quantum coherent measurement on the output of the line and the recursive processing by Kalman-Busy filter. All the results are illustrated by an example of the optimal control problem for a quantum open oscillator at the input of a quantum wave transmission line.