Nondemolition filters for quantum systems

The paper is concerned with the formulation of a continuous-time quantum-mechanical filter. In a previous paper (Ong et al., 1984), the invertibility of a quantum system coupled to a weak time-dependent classical field was studied. The physical system is modeled as an infinite-dimensional bilinear system. Necessary and sufficient conditions of invertibility were derived under the assumption that the output observable is a quantum nondemolition observable (QNDO), characterized by the classical property that its expected value is equal to its measured value. In this paper necessary and sufficient conditions are developed for an observable to qualify as a QNDO; if in addition the criteria for invertibility are met, the given observable defines a quantum nondemolition filter (QNDF). The associated filtering algorithm thus separates cleanly into the choice of output observable (a QNDO) and the choice of procedure for processing the measurement outcomes. This approach has the advantage over previous schemes that no optimization is necessary. Applications to demodulation of optical signals and to the detection and monitoring of gravitational waves are envisioned.