Dokument: Discrimination of mixed quantum states: Reversible maps and unambiguous strategies

Titel:	Discrimination of mixed quantum states: Reversible maps and unambiguous strategies
URL für Lesezeichen:	https://docserv.uni-duesseldorf.de/servlets/DocumentServlet?id=8238
URN (NBN):	urn:nbn:de:hbz:061-20080709-114428-5
Kollektion:	Dissertationen
Sprache:	Englisch
Dokumententyp:	Wissenschaftliche Abschlussarbeiten » Dissertation
Medientyp:	Text
Autor:	Kleinmann, Matthias [Autor]
Dateien:	[Dateien anzeigen] Adobe PDF [Details] 12,66 MB in einer Datei [ZIP-Datei erzeugen] Dateien vom 08.07.2008 / geändert 08.07.2008
Beitragende:	Prof. Dr. Bruß, D. [Gutachter] Prof. Dr. Egger, Reinhold [Gutachter] Prof. Dr. Lütkenhaus, Norbert [Gutachter]
Dewey Dezimal-Klassifikation:	500 Naturwissenschaften und Mathematik » 530 Physik
Beschreibung:	The discrimination of two mixed quantum states is a fundamental task in quantum state estimation and quantum information theory. In quantum state discrimination a quantum system is assumed to be in one of two possible – in general mixed – non-orthogonal quantum states. The discrimination then consists of a measurement strategy that allows to decide in which state the system was before the measurement. In unambiguous state discrimination the aim is to make this decision without errors, but it is allowed to give an inconclusive answer. Especially interesting are measurement strategies that minimize the probability of an inconclusive answer. A starting point for the analysis of this optimization problem was a result by Eldar et al. [Phys. Rev. A 69, 062318 (2004)], which provides non-operational necessary and sufficient conditions for a given measurement strategy to be optimal. These conditions are reconsidered and simplified in such a way that they become operational. The simplified conditions are the basis for further central results: It is shown that the optimal measurement strategy is unique, a statement that is e.g. of importance for the complexity analysis of optimal measurement devices. The optimal measurement strategy is derived for the case, where one of the possible input states has at most rank two, which was an open problem for many years. Furthermore, using the optimality criterion it is shown that there always exists a threshold probability for each state, such that below this probability it is optimal to exclude this state from the discrimination strategy. If the two states subject to discrimination can be brought to a diagonal structure with (2×2)-dimensional blocks, then the unambiguous discrimination of these states can be reduced to the unambiguous discrimination of pure states. A criterion is presented that allows to identify the presence of such a structure for two self-adjoint operators. This criterion consists of the evaluation of three commutators and allows an explicit construction of the (2×2)-dimensional blocks. As an important application of unambiguous state discrimination, unambiguous state comparison, i.e., the question whether two states are identical or not, is generalized and optimal measurements for this problem are constructed. If for a certain family of states, a physical device maps the input state to an output state, such that a second device can be built that yields back the original input state, such a map is called reversible on this family. With respect to state discrimination, such reversible maps are particularly interesting, if the output states are pure. A complete characterization of all families that allow such a reversible and purifying map is provided. If the states are mapped to pure states, but the map itself is not reversible, upper and lower bounds are analyzed for the “deviation from perfect faithfulness”, a quantity which measures the deviation from a reversible mapping.
Lizenz:	Urheberrechtsschutz
Fachbereich / Einrichtung:	Mathematisch- Naturwissenschaftliche Fakultät » WE Physik » Theoretische Physik
Dokument erstellt am:	08.07.2008
Dateien geändert am:	08.07.2008
Promotionsantrag am:	09.05.2008
Datum der Promotion:	30.06.2008