Symmetric extension of bipartite quantum states and its use in quantum key distribution with two-way postprocessing [Elektronische Ressource] / vorgelegt von Geir Ove Myhr
Symmetric extension of bipartite quantum statesand its use in quantum key distributionwith two-way postprocessingDer Naturwissenschaftlichen Fakult atder Friedrich-Alexander-Universit at Erlangen-Nurn bergzurErlangung des Doktorgrades Dr. rer. nat.vorgelegt vonGeir Ove Myhraus OsloAls Dissertation genehmigt von derNaturwissenschaftlichen Fakult at derUniversit at Erlangen-Nurn bergTag der mundlic hen Prufung: 08/11/2010Vorsitzender der Promotionskommission: Prof. Dr. Rainer FinkErstberichterstatter: Prof. Dr. Norbert Lutk enhausZweitberichterstatter: Prof. Dr. Andreas KnaufSummaryJust like we can divide the set of bipartite quantum states into separable statesand entangled states, we can divide it into states with and without a symmetricextension. The states with a symmetric extension|which includes all the separa-ble states|behave classically in many ways, while the states without a symmetricextension|which are all entangled|have the potential to exhibit quantum e ects.The set of states with a symmetric extension is closed under local quantum oper-ations assisted by one-way classical communication (1-LOCC) just like the set ofseparable states is closed under local operations assisted by two-way classical com-munication (LOCC). Because of this, states with a symmetric extension often playthe same role in a one-way communication setting as the separable states play in atwo-way communication setting.