Continuous Observation of Quantum Systems

Abstract

We review a general theory to describe the nonunitary evolution of quantum systems under measurement, which is the main subject of the first part of this Thesis. Quantum measurement theory provides us with a theoretical framework to discuss how a quantum system exhibits an unavoidable change due to a measurement process. In particular, theory of continuous measurements gives a unified description to study the nonunitary dynamics of quantum systems subject to weak and frequent repeated measurements. In Sect. 2.1, we formulate a quantum measurement process based on an indirect measurement model and review its mathematical property. In Sect. 2.2, we apply it to formulate a theory of continuous observations, in which measurements are performed continuously in time.