Quantum nondemolition measurements via quantum counting

For a harmonic-oscillator gravitational-wave detector, we show that a quantum nondemolition measurement of the square of the number operator may be made by coupling the detector to an oscillator readout via a quadratic interaction, as in optical four-wave mixing. Explicit evaluation of the effect of a meter readout on the detector demonstrates the possibility of arbitrarily accurate instantaneous measurements for sufficiently large coupling strength.