Unambiguous State Discriminationof two density matricesin Quantum Information TheoryDen Naturwissenschaftlichen Fakulta¨tender Friedrich-Alexander-Universita¨t Erlangen-Nu¨rnbergzurErlangung des Doktorgradesvorgelegt vonPhilippe Raynalaus Lyon, FrankreichiiQuantum Information Theory GroupTheoretische Physik ILehrstuhl fu¨r OptikInstitut fu¨r Optik, Information und PhotonikMax Planck ForschungsgruppeErlangen 2006iiiAls Dissertation genehmigt von den naturwissenschaftlichen Fakulta¨ten der Universita¨tErlangen-Nu¨rnbergTag der mu¨ndlichen Pru¨fung: 16.08.2006Vorsitzender der Promotionskommission: Prof. Dr. D. P. Ha¨derErstberichterstatter: Prof. Dr. N. Lu¨tkenhausZweitberichterstatter: Prof. Dr. D. BrußivAbstractQuantum state discrimination is a fundamental task in quantum information theory. The signalsare usually nonorthogonal quantum states, which implies that they can not be perfectly distin-guished. One possible discrimination strategy is the so-called Unambiguous State Discrimination(USD) where the states are successfully identified with non-unit probability, but without error.The optimal USD measurement has been extensively studied in the case of pure states, especiallyfor any pair of pure states. Recently, the problem of unambiguously discriminating mixed quan-tum states has attracted much attention. In the case of a pair of generic mixed states, no completesolution is known.