Path Integrals over Measurement Amplitudes: Practical Quantum Foundations for Signal Processing and Control

It is shown that classical control diagrams can be mapped one-to-one onto quantum path integrals over measurement amplitudes. To show the practical utility of this method, exact closed-form expressions are derived for the control dynamics and quantum noise levels of a test mass observed by a Fabry-Perot interferometer. This formalism provides an efficient yet rigorous method for analyzing complex systems such as interferometric gravity wave detectors and magnetic resonance force microscopy (MRFM) experiments. Quantum limits are conjectured for the sensitivity of interferometric observation of test mass trajectories.