Exact Controllability for Stochastic Schrodinger Equations

This paper is addressed to studying the exact controllability for stochastic Schr\"{o}dinger equations by two controls. One is a boundary control in the drift term and the other is an internal control in the diffusion term. By means of the standard duality argument, the control problem is converted into an observability problem for backward stochastic Schr\"{o}dinger equations, and the desired observability estimate is obtained by a global Carleman estimate. At last, we give a result about the lack of exact controllability, which shows that the action of two controls is necessary.