Observability Estimate for Stochastic Schroedinger Equations

In this paper, we establish a boundary observability estimate for stochastic Schr"{o}dinger equations by means of the global Carleman estimate. Our Carleman estimate is based on a new fundamental identity for a stochastic Schr"{o}dinger-like operator. Applications to the state observation problem for semilinear stochastic Schr"{o}dinger equations and the unique continuation problem for stochastic Schr"{o}dinger equations are also addressed.