Witnessing entanglement in qudit systems [Elektronische Ressource] / von Philipp Hyllus

Witnessing entanglementin qudit systemsVom Fachbereich Physik der Universit at Hannoverzur Erlangung des GradesDoktor der NaturwissenschaftenDr. rer. nat.genehmigte DissertationvonMSc Philipp Hyllusgeboren am 4. Mai 1976 in Wolfenbuttel in Niedersachsen2005Referent: Prof. Dr. M. LewensteinKorreferentin: Prof. Dr. D. Bru Tag der Promotion: 17. Januar 2005AbstractIn this thesis, we deal with several aspects of the theory of entanglement, all of whichare connected to the problem of nding ways to witness the presence of entanglementin a system of qudits, i.e., d-level quantum systems.After having recalled some basic facts and de nitions concerning the theory of entan-glement, we concentrate on the local detection of entanglement via witness operators.A negative expectation value of these operators signals the presence of entanglementbecause their expectation value is positive with respect to all separable states. Wediscuss known ways and introduce a new simple method to construct witnesses. Inthis form, they are not easily applicable in an experiment, because they requiremeasurements on the total system. Thus, we construct local decompositions suchthat the witnesses can be measured with local measurements only, and minimizethe number of local measurements necessary. We concentrate on witnesses in highdimensional bipartite systems, and on witnesses for bound entanglement, a weakform of entanglement, also in multipartite systems.