Exact controllability for stochastic Schrödinger equations

This paper is addressed to studying the exact controllability of stochastic Schrödinger equations by two controls. One is a boundary control and the other is an internal control in the diffusion term. By means of the duality argument, the control problem is converted into an observability problem for backward stochastic Schrödinger 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.