You need JavaScript to view this

Characterizing quantum correlations. Entanglement, uncertainty relations and exponential families

Abstract

This thesis is concerned with different characterizations of multi-particle quantum correlations and with entropic uncertainty relations. The effect of statistical errors on the detection of entanglement is investigated. First, general results on the statistical significance of entanglement witnesses are obtained. Then, using an error model for experiments with polarization-entangled photons, it is demonstrated that Bell inequalities with lower violation can have higher significance. The question for the best observables to discriminate between a state and the equivalence class of another state is addressed. Two measures for the discrimination strength of an observable are defined, and optimal families of observables are constructed for several examples. A property of stabilizer bases is shown which is a natural generalization of mutual unbiasedness. For sets of several dichotomic, pairwise anticommuting observables, uncertainty relations using different entropies are constructed in a systematic way. Exponential families provide a classification of states according to their correlations. In this classification scheme, a state is considered as k-correlated if it can be written as thermal state of a k-body Hamiltonian. Witness operators for the detection of higher-order interactions are constructed, and an algorithm for the computation of the nearest k-correlated state is developed.
Authors:
Publication Date:
Apr 20, 2012
Product Type:
Thesis/Dissertation
Report Number:
INIS-DE-1355
Resource Relation:
Other Information: TH: Diss. (Dr.rer.nat.)
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; BELL THEOREM; COMMUTATION RELATIONS; CORRELATIONS; ENTROPY; ERRORS; HAMILTONIANS; MANY-BODY PROBLEM; PHOTONS; QUANTUM ENTANGLEMENT; QUANTUM MECHANICS; SPIN ORIENTATION; STABILIZATION; UNCERTAINTY PRINCIPLE
OSTI ID:
22007189
Research Organizations:
Siegen Univ. (Germany). Naturwissenschaftlich-Technische Fakultaet
Country of Origin:
Germany
Language:
English
Other Identifying Numbers:
TRN: DE12FC750
Availability:
Commercial reproduction prohibited. Available from ETDE as OSTI ID: 22007189;
Submitting Site:
DEN
Size:
133 page(s)
Announcement Date:
Dec 22, 2012

Citation Formats

Niekamp, Soenke. Characterizing quantum correlations. Entanglement, uncertainty relations and exponential families. Germany: N. p., 2012. Web.
Niekamp, Soenke. Characterizing quantum correlations. Entanglement, uncertainty relations and exponential families. Germany.
Niekamp, Soenke. 2012. "Characterizing quantum correlations. Entanglement, uncertainty relations and exponential families." Germany.
@misc{etde_22007189,
title = {Characterizing quantum correlations. Entanglement, uncertainty relations and exponential families}
author = {Niekamp, Soenke}
abstractNote = {This thesis is concerned with different characterizations of multi-particle quantum correlations and with entropic uncertainty relations. The effect of statistical errors on the detection of entanglement is investigated. First, general results on the statistical significance of entanglement witnesses are obtained. Then, using an error model for experiments with polarization-entangled photons, it is demonstrated that Bell inequalities with lower violation can have higher significance. The question for the best observables to discriminate between a state and the equivalence class of another state is addressed. Two measures for the discrimination strength of an observable are defined, and optimal families of observables are constructed for several examples. A property of stabilizer bases is shown which is a natural generalization of mutual unbiasedness. For sets of several dichotomic, pairwise anticommuting observables, uncertainty relations using different entropies are constructed in a systematic way. Exponential families provide a classification of states according to their correlations. In this classification scheme, a state is considered as k-correlated if it can be written as thermal state of a k-body Hamiltonian. Witness operators for the detection of higher-order interactions are constructed, and an algorithm for the computation of the nearest k-correlated state is developed.}
place = {Germany}
year = {2012}
month = {Apr}
}