Sequential Quantum Measurements - Tammero, Tuomas (My University, 2018)
This thesis studies the field of quantum measurements and more precisely sequential measurements. The aim is to provide answers to questions like when is performing a sequential or a repeated measurement meaningful, or even possible. This is important in order to understand what type of information can be acquired when performing measurements on quantum states. In basic quantum theory observables are identified with self-adjoint operators. We introduce the concept of a positive operator valued measure (POVM) to gain better understanding on observables. The downside to POVMs is that they don't produce a new state after the measurement, only measurement statistics. In order to perform multiple measurements on a quantum state, the concepts of measurement model and instrument are defined in this thesis. Using instruments to perform measurements is essential in order to describe a state after the initial measurement is performed. This way it's possible to make measurements sequentially. After defining the necessary tools for sequential measurements and a few different properties related to them, some applicable situations for these kind of measurements are shown. This way sequential measurements end up being somewhat meaningful in order to gain information from quantum systems.
Keywords: Measurement, Sequential Measurement, Observable, Measurement Model, Instrument