Verschrankungsnachweise¨mit Anwendungen in derQuantenkommunikationDen Naturwissenschaftlichen Fakultaten¨der Friedrich-Alexander-Universitat¨ Erlangen-Nurnber¨ gzurErlangung des Doktorgrades Dr. rer. nat.vorgelegt vonHauke Haseler¨aus Tonning¨iiAls Dissertation genehmigt von denNaturwissenschaftlichen Fakultaten¨ derUniversitat¨ Erlangen-Nurnber¨ gTag der mundlichen¨ Prufung:¨ 16/02/2010Vorsitzender der Promotionskommission: Prof. Dr. Eberhard Bansch¨Erstberichterstatter: Prof. Dr. Norbert Lutk¨ enhausZweitberichterstatter: Prof. Dr. Paul-Gerhard ReinhardiiiQuantum Information Theory GroupTheoretische Physik ILehrstuhl fur¨ OptikInstitut fur¨ Optik, Information und PhotonikMax Planck ForschungsgruppeErlangen 2010ivvSummaryIn this thesis, we investigate the uses of entanglement and its verification in quantum commu-nication. Typically, it is the presence of which allows quantum communicationprotocols to outperform their classical counterparts, or to achieve tasks which are infeasible withclassical physics. Therefore, the verification of entanglement can provide fundamental tests tocertify that experimental implementations of such protocols operate quantum mechanically. Themain object here is to develop a verification procedure which is adaptable to a wide range ofapplications, and whose implementation has low requirements on experimental resources. Wepresent such a procedure in the form of the Expectation Value Matrix.