This thesis is devoted to the study of the quantum trajectories obtained from the theory of continuous measurement in non relativistic quantum mechanics. New theoretical results as well as examples of applications are presented. On the theoretical front, we study mostly the limit of "strong" measurement where we put forward the emergence of quantum jumps and quantum spikes, two phenomena we characterize in detail. Out of the strong measurement limit, we investigate a method to extract information from a register of qubits optimally. On the application front, we introduce an original method to control quantum systems exploiting only the freedom of changing the measurement intensity and we explain the transition between a ballistic and a diffusive behavior in open quantum random walks; two byproduct of the theoretical study of the strong measurement regime. We further study the problem of semi-classical gravity and show that continuous measurement theory allows to construct a consistent model in the Newtonian regime. We eventually suggest possible extensions of the formalism to a posteriori estimation and hint at generalizations of the results for the strong measurement limit in the wider context of discrete repeated measurements. In the course of our presentation, we emphasize the link with other approaches to the theory of continuous measurement (parallels with stochastic filtering and collapse models in foundations) rather than aim for mathematical rigor.
This chapter explores accurate formulation of the approach, including a description of the evolution of the measured system and the generalized unitarity condition for this evolution. It argues that evolution under continuous measurement has both quantum and classical features. The chapter deals with the evolution of the system subject to continuous measurement. It demonstrates in general form and considers the specific example of a free particle scattered because its position is measured. The quantum theory of measurements has been discussed not only because of its conceptual interest but also for practical purposes. The chapter discusses the application of the measurement amplitude for estimation of probabilities of different measurement outputs. However, the same amplitude can be used to describe the evolution of the system subject to the measurement. The chapter shows the continuous measurement changes the evolution of the quantum system undergoing the measurement.