State and dynamical parameter estimation for open quantum systems - art. no. 042105

Following evolution of an open quantum system one requires full knowledge o f its dynamics. In this paper we consider open quantum systems for which th e Hamiltonian is "uncertain." In particular, we treat in detail a simple sy stem similar to that considered by Mabuchi [Quant. Semiclass. Opt. 8, 1103 (1996)]: a radiatively damped atom driven by an unknown Rabi frequency il ( as would occur for an atom at an unknown point in a standing light wave). B y measuring the environment of the system, knowledge about the system state , and about the uncertain dynamical parameter, can be acquired. We find tha t these two sorts of knowledge acquisition (quantified by the posterior dis tribution for Omega, and the conditional purity of the system, respectively ) are quite distinct processes, which are not strongly correlated. Also, th e quality and quantity of knowledge gain depend strongly on the type of mon itoring scheme. We compare five different detection schemes (direct, adapti ve, homodyne of the x quadrature, homodyne of the y quadrature, and heterod yne) using four different measures of the knowledge gain (Shannon informati on about Omega, variance in Omega, long-time system purity, and short-time system purity).