A control problem for Gaussian states

This paper is concerned with an analysis of physical limitations of macrosc opic control due to the laws of quantum mechanics. A control problem for a class of quantum states, called Gaussian, which are widely used in quantum optics is considered. Our interest is focused on controlling the mean value and the variance of two obsevables, coordinate and momentum,with respect t o Gaussian states. A necessary and sufficient condition for the mean value to be controllable is obtained. Furthermore it is shown that a problem to a ttain the smallest possible variance under the condition that its mean valu e is stable is reduced to an optimal regulator problem.