STATE ESTIMATION WITH SUCCESSIVE MEASUREMENTS AND BAYESIAN ANALYSIS OF BELL EXPERIMENTS

Abstract

This thesis studies two basic topics: state estimation with successive measurements and Bayesian analysis of Bell experiments. We first study a novel scheme for quantum state estimation based on successive measurements. We derive the general expression for the probability of obtaining a sequence of clicks.. Then we apply our method to the data from a micromaser experiment. We reconstruct the initial photon number distribution, which is in perfect agreement with the expected Poisson distribution. The second part of this thesis is about the analysis of Bell experiments by Bayesian inference. Here we use the relative belief ratio (RB) as a measure of evidence, which is the ratio between posterior probability and prior probability. If the RB of a region is larger than 1, the data provide evidence in favor of it. Otherwise, it's evidence against. We analyze the data from four loophole-free Bell experiments. We find for the two photon experiments the stated values of the down-conversion rate are not correct. We confirm that there is no bias in favor of QM in our prior. For all data, we find very strong evidence in favor of QM and against LHV.