On the principle of quantum nondemolition measurements

A generalization of the principle of quantum nondemolition measurements is proposed. Its essence reduces to measuring a commuting family of observables on a certain extension of the original system, the extension including an auxiliary independent system. The advantages of such a generalization are demonstrated by the simple example of estimating the force acting on a quantum oscillator, for which the principle makes it possible to obtain the optimal estimate. The connection between the principle of quantum nondemolition measurement and the scheme of repeated measurements in the quantum theory of open systems is investigated.