Fisher information in Quantum Theory

Abstract

Fisher information which is an important concept in statistical estimation theory and information theory provides a measurement of a disorder system which is specified by a corresponding probability the likelihood Fisher information is related to the Kullback-Leibler entropy satisfies the Cram?r-Rao inequality and is also related to statistical distance In this thesis we provide a bridge to connect classical and quantum mechanics by using Fisher information Following the principle of minimum Fisher information we describe the mechanism of quantum world — the Schr?dinger equation from the Hamilton-Jacobi equation For a given metric g?ν which is identified as Fisher information metric we generate new constraints for the probability distributions for physical systems We postulate the existence of intrinsic probability distributions for physical systems and calculate the probability distribution by optimizing the Fisher information metric under specified constraints Accordingly we get differential equations for the probability distributions

Date of Award	2014 Jul 16
Original language	English
Supervisor	Su-Long Nyeo (Supervisor)