Detecting quantum entanglement [Elektronische Ressource] : entanglement witnesses and uncertainty relations / von Otfried Gühne

Detecting Quantum Entanglement:Entanglement WitnessesandUncertainty RelationsVom Fachbereich Physik der Universit at Hannoverzur Erlangung des Grades einesDoktors der NaturwissenschaftenDr. rer. nat.genehmigte DissertationvonDipl.-Phys. Otfried Guhne?geboren am 15. Mai 1975 in Munster? in Westfalen2004Referent: Prof. Dr. M. LewensteinKorreferentin: Priv.-Doz. Dr. D. BrußTag der Promotion: 1. Juli 2004AbstractThis thesis deals with methods of the detection of entanglement. After recallingsome facts and definitions concerning entanglement and separability, we investigatetwo methods of the detection of entanglement.In the first part of this thesis we consider so-called entanglement witnesses,mainly in view of the detection of multipartite entanglement. Entanglement wit-nessesareobservablesforwhichanegativeexpectationvalueindicatesent.We first present a simple method to construct these witnesses. Since witnesses arenonlocal observables, they are not easy to measure in a real experiment. However,as we will show, one can circumvent this problem by decomposing the witness intoseveral local observables which can be measured separately. We calculate the localdecompositionsforseveralinterestingwitnessesfortwo,threeandfourqubits. Local can be optimized in the number of measurement settings which areneeded for an experimental implementation.