- Thesis:
- Master in Mathematics
- Author:
- Henning Stein
- Title:
- Local asymptotic equivalence of pure states ensembles and quantum Gaussian white noise
- Supervisor:
- Jan JOHANNES
- Abstract:
- The purpose of this thesis is twofold. Firstly, its aim is to serve as a starting point for beginners in quantum theory and introduce the fundamental quantum statistical concepts in a compact and concise manner. As such, in the first half, we present the main notions of quantum statistic that consist of the thoeretical physical definitions and their statistical application. Here, we try to highlight both the parallels and differences of this theory to the classical case. Secondly, we will apply these definitions to proof a local asymptotic equivalence of a quantum i.i.d. and a quantum Gaussian white noise model, that are both counterparts of the classical nonparametric models. We will use this result to proof minimax rates for the estimation of pure states and the estimation of a quadratic functional as well as proving a parametric rate in the nonparametric testing problem for a pure state in a Hermite-Sobolev-class.
- Reference:
- C. Butucea, M. Guță, et M. Nussbaum Local asymptotic equivalence of pure states ensembles and quantum gaussian white noise, The Annals of Statistics, 46(6B):3676-3706 2018
| Statistics Group | Institute for Mathematics | Faculty of Mathematics and Computer Science | University Heidelberg |