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On the experimental generation and characterization of entangled states of light [Elektronische Ressource] / James DiGuglielmo

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On the Experimental Generation and Characterizationof Entangled States of LightVon der Fakult¨at fu¨r Mathematik und Physikder Gottfried Wilhelm Leibniz Universit¨at Hannoverzur Erlangung des GradesDoktor der Naturwissenschaften– Dr. rer. nat. –genehmigte DissertationvonDipl.-Phys. James DiGuglielmogeboren am 22. April 1982 in Belleville, New JerseyVereinigte Staaten von Amerika2010Referent: Prof. Dr. Roman SchnabelKorreferent: Prof. Dr. Karsten DanzmannTag der Promotion: 15.07.2010iiAbstractShared entanglement combined with local operations and classical communication can beused as the physical resource for a communication channel. It is therefore important todevelop the experimental techniques to prepare various multipartite entangled states andcharacterize their entanglement properties. Additionally, since all experimental results in-volve statistical uncertainty, methods to estimate this uncertainty and propagate it throughfurther calculations is essential for any proof-of-principle experiment.The first set of experimental results to be presented involves the preparation and char-acterization of various classes of bipartite quadrature entanglement. These states are recon-structed by measuring the full 44 covariance matrix and evaluating from it informationtheoretic quantities such as the raw secret key rate, the quantum channel capacity and theteleportation fidelity for coherent states.

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Published 01 January 2010
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On the Experimental Generation and Characterization
of Entangled States of Light
Von der Fakult¨at fu¨r Mathematik und Physik
der Gottfried Wilhelm Leibniz Universit¨at Hannover
zur Erlangung des Grades
Doktor der Naturwissenschaften
– Dr. rer. nat. –
genehmigte Dissertation
von
Dipl.-Phys. James DiGuglielmo
geboren am 22. April 1982 in Belleville, New Jersey
Vereinigte Staaten von Amerika
2010Referent: Prof. Dr. Roman Schnabel
Korreferent: Prof. Dr. Karsten Danzmann
Tag der Promotion: 15.07.2010iiAbstract
Shared entanglement combined with local operations and classical communication can be
used as the physical resource for a communication channel. It is therefore important to
develop the experimental techniques to prepare various multipartite entangled states and
characterize their entanglement properties. Additionally, since all experimental results in-
volve statistical uncertainty, methods to estimate this uncertainty and propagate it through
further calculations is essential for any proof-of-principle experiment.
The first set of experimental results to be presented involves the preparation and char-
acterization of various classes of bipartite quadrature entanglement. These states are recon-
structed by measuring the full 44 covariance matrix and evaluating from it information
theoretic quantities such as the raw secret key rate, the quantum channel capacity and the
teleportation fidelity for coherent states. The connection between the quantity of entangle-
ment and its utility as a communication channel is numerically explored.
Thenextexperiment focusesonanewstatisticalscheme basedontheBayesianparadigm
for quantum state reconstruction. The key result of this work is the calculation of error-
bars in the form of a probability distribution known as the posterior distribution on the
reconstructed Wigner function for phase-diffused squeezed states. The method relies on
the Markov chain Monte Carlo algorithm to draw samples from the posterior distribution.
Since these samples contain all of the relevant statistical information with regard to the
reconstruction, probability distributions can be derived for quantities, such as the state
purity, without having to make additional assumptions as to the distributional form of the
statistical uncertainties.
Finally,theexperimentaldemonstrationofGaussianboundentangledstatesispresented.
Continuous-variableboundentanglementisanexampleofafourpartymixedentangledstate,
whose preparation requires precise control over a network of interference beam splitters, ho-
modyne detectors and nonlinear optical cavities. The experimental and feedback control
techniques required for this task are explained and illustrated using results from the labora-
tory. Finally,theexperimentaldemonstrationofboundentanglementispresentedalongwith
adiscussion ofthe dataanalysis methods andpossible improvements forfutureexperiments.
Having demonstrated the capability to control multimode entangled states, it becomes
possible to explore various other types of multipartite entangled states for both quantum
communication and quantum computing.
Keywords: Mutlipartite entanglement, Bound Entanglement, Quantum State Recon-
struction.
iiiZusammenfassung
Verschra¨nkte Zust¨ande bilden zusammen mit lokalen Operationen und klassischer Kommu-
nikation die physikalische Grundlage eines Quantenkommunikationskanals. Deshalb sind die
Entwicklung von experimentellen Techniken zur Herstellung unterschiedlicher verschra¨nkter
Zusta¨nde sowie ihre Charakterisierung von besonderer Bedeutung.
Da alle Experimente, unter anderem sogenannte “proof-of-principle” Versuche, durch
statistische Ungewissheit begrenzt sind, ist auch die Entwicklung von Methoden der Fehler-
analyse wichtig. Beginnend mit der Charakterisierung der freien Verschra¨nkung wird der
Zusammenhang zwischen der Verteilung verschra¨nkter Zusta¨nde und der Quantenkommu-
nikation theoretisch wie auch experimentell dargestellt. Die vollst¨andige Messung der Ko-
varianzmatrix diverser verschra¨nkter Zusta¨nde liefert Einsichten in Informationen wie die
Kapazita¨tdes Quantenkanals(quantum channel capacity), dieQuantengenauigkeit (fidelity)
und andere.
FernerwurdeeinneuesBayes’schesVerfahrenzurQuantenzustandsrekonstruktioneingefu¨hrt.
Diesesermo¨glichtes,dieFehlereinerRekonstruktionausdersogenanntenPosteriorVerteilung
mithilfedesMarkovchainMonteCarloAlgorithmuszuberechnen. Dasomitdievollst¨andige,
statistische Information der Rekonstruktion vorliegt, ko¨nnen weitere Eigenschaften des Zu-
standes wie z.B. die Reinheit ohne zusa¨tzliche Annahmen bestimmt werden.
Schlussendlich wird der experimentelle Nachweis Gaußscher gebundener Verschra¨nkung
dargestellt. Die Erzeugung fand im Regime kontinuierlicher Variablen statt und beno¨tigte
neben linearen Elementen wie Phasenschiebern, Interferenzstrahlteilern und Homodynde-
tektoren auch nicht-lineare Resonatoren und genaue Reglungstechniken. Diese Methoden
sind anhand der experimentellen Ergebnisse beschrieben. Der experimentelle Nachweis der
gebundenen Verschra¨nkung wird auch im Rahmen der Datenanalyse diskutiert.
DieHerstellungvonMehrmodenVerschra¨nkungermo¨glichtdieUntersuchungverschiedener
Arten von Verschra¨nkung fu¨r die Quantenkommunikation bzw. den Quantencomputer.
Schlu¨ßelwo¨rter: gebundeneVerschra¨nkung,Quantenzustandsrekonstruktion, Mehrmoden
Verschra¨nkung.
vList of Publications
J. DiGuglielmo, B. Hage, A. Franzen, J. Fiur´a˘sek, and R. Schnabel, Experimental
characterization of gaussian quantum-communication channels, Physical Review A76
(2007), 012323.
J. DiGuglielmo, C. Messenger, J. Fiur´a˘sek, B. Hage, A. Samblowski, T. Schmidt, and
R. Schnabel, Markov chain monte carlo reconstruction of quantum states, Physical
Review A 79 (2009), 032114.
A. Franzen, B. Hage, J. DiGuglielmo, J. Fiur´a˘sek, and R. Schnabel, Experimental
demonstration of continuous variable purification of squeezed states, Physical Review
Letters 97 (2006), 150505.
B. Hage, A. Franzen, J. DiGuglielmo, P. Marek, J. Fiur´a˘sek, and R. Schnabel, On the
distillation and purification of phase-diffused squeezed states, New Journal of Physics
9 (2007), 227.
B. Hage, A. Samblowski, J. DiGuglielmo, A. Franzen, J. Fiur´a˘sek, and R. Schn-
abel, Preparation of distilled and purified continuous-variable entangled states, Nature
Physics 4 (2008), 915.
T. Kiesel, W. Vogel, B. Hage, J. DiGuglielmo, A. Samblowski, and R. Schnabel, Ex-
perimental test of nonclassicality criteria for phase-diffused squeezed states, Physical
Review A 79 (2009), 022122.
P.Marek,J.Fiur´a˘sek,B.Hage,A.Franzen,J.DiGuglielmo,andR.Schnabel, Multiple-
copy distillation and purification of phase-diffused squeezed states, Physical Review A
76 (2007), 053820.
vii