Nonperturbing measurement in a gravitational wave experiment

In connection with the problem of increasing the sensitivity of gravitational wave experiments a study is made of the quantum restrictions which may arise in measurements of the classical force on the basis of the response of a quantum oscillator. Attention is paid to a class of nonperturbing measurements which is free of the quantum restrictions on the accuracy of measurement of the force. It is shown that the measurement can be realized on observation of operators which are quantum integrals of motion of the system under investigation. The physical causes which are responsible for the presence or absence of a quantum limit of sensitivity for an arbitrary choice of the observable and which are contained in the degree of indeterminancy of the initial state of the system are determined. In the case of integrals of motion the indeterminancy may be reduced to zero as a result of the first exact measurement and subsequently remain zero (quasi-nonperturbing measurement). It is shown furthermore that it is possible to choose a set of observables which in general do not depend on the initial state of the quantum system but retain the information on the external action. An exact continuous measurement in this case can be realized without any special preparation of the state of the system (strictly nonperturbing measurement). The general rule for setting up such optimal variables is the same as that in the quantum theory of filtration