A control problem for gaussian states
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This paper is concerned with an analysis of physical limitations of macroscopic 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 to Gaussian states. A necessary and sufficient condition for the mean value to be controllable is obtained. Furthermore it is shown that a problem to attain the smallest possible variance under the condition that its mean value is stable is reduced to an optimal regulator problem.
KeywordsHilbert Space Quantum Mechanic Control Problem Quantum State Uncertainty Relation
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