QUANTUM DETECTION AND PARAMETER ESTIMATION FOR CONTINUOUSLY MEASURED SYSTEMS

Abstract

Many measurement schemes of quantum systems involve coupling of the system to an electromagnetic field, which is then measured continuously. This includes qubit systems, such as nitrogen-vacancy centers, as well as mechanical systems, such as cavity optomechanics. In this thesis, we study the problem of detection and estimation for quantum systems that are measured continuously. A signal processing architecture for qubit readout is proposed to determine the initial state of a qubit. We consider both Gaussian and Poissonian noise models and derive analytical solutions to our protocol, which should be useful for fast feedback control and error correction purposes. We also propose a framework of spectrum-parameter estimation for stochastic processes using quantum dynamical systems, proving fundamental limits and investigating measurement and data analysis techniques that approach the limits. Lastly, we discuss our attempt at generalizing the framework of spectrum-parameter estimation to include quantum stochastic processes.