Quantum Teleportation and Multi-photon Entanglement Dissertation zur Erlangung des Grades eines Doktors der Naturwissenschaften eingereicht von M.Sc. Jian-Wei Pan University of Science and Technology of China Durchgef¨uhrt am Institut f¨ur Experimentalphysik der Universit¨at Wien bei o.Univ.Prof.Dr. Anton Zeilinger Gef¨ordert vom Fonds zur F¨orderung der wissenschaftlichen Forschung,Projekte S6502 und F1506 und durch das TMR-Netzwerk The Physics of Quantum Information der Europ¨aischen Kommission. Contents 1 Introduction 5 2 Manipulation of Entangled States 10 2.1 Quantum network and its applications ............. 11 2.2 Practical schemes for entangled-state analysis ......... 15 2.2.1 Bell-state analysis ..................... 16 2.2.2 GHZ-state analyzer .................... 20 2.3 Polarization-entangled photon pairs ............... 29 3 Quantum Teleportation 33 3.1 Introduction ............................ 33 3.2 Quantum teleportation–the idea ................. 34 3.2.1 The problem ........................ 34 3.2.2 The concept of quantum teleportation ......... 35 3.3 Experimental teleportation .................... 40 3.3.1 Experimental scheme ................... 40 3.3.2 Results ........................... 43 3.4 Discussion ............................. 50 4 Entanglement Swapping 53 4.1 Introduction ............................ 53 4.2 Theoretical scheme ........................ 54 i ii CONTENTS 4.3 Experimental entanglement swapping .............. 56 4.4 Generalization and applications ................. 61 5 Three-photon GHZ entanglement 64 5.1 Introduction ............................ 64 5.2 Experimental Set-up ....................... 65 5.3 Observation of three-photon entanglement ........... 72 5.4 Discussion and conclusion .................... 75 6 Experimental tests of the GHZ theorem 76 6.1 Introduction ............................ 76 6.2 The conflict with local realism .................. 77 6.2.1 GHZtheorem ....................... 77 6.2.2 Generalization to conditional GHZstate ........ 81 6.3 Experimental results ....................... 84 6.4 Discussion and Prospects ..................... 90 7 Conclusions and outlook 92 Zusammenfassung Die vorliegende Dissertation ist das Ergebnis theoretischer und experimenteller Arbeitenuber ¨ die Physik von Mehrteilcheninterferenz. Die theoretischen Ergebnisse zeigen, daß man Quantenverschr¨ankung mit einem Quantennet- zwerk aus einfachen Quantenlogikgattern und einer kleinen Anzahl von Qubits kontrollieren und manipulieren kann. Da es bis jetzt keine experimentelle Durchf¨uhrung von Quantengattern f¨ur zwei unabh¨angig erzeugte Photonen gibt, pr¨asentieren wir hier eine realisierbare Methode, verschr¨ankte Viel- teilchenzust¨ande zu erzeugen und zu identifizieren. In der experimentellen Arbeit wurden die zum Studium von neuarti- gen Vielteilcheninterferenzph¨anomenen n¨otigen Techniken von Grund auf en- twickelt. Wir berichten in dieser Arbeituber ¨ die erstmalige experimentelle Realisierung von Quantenteleportation, ’Entanglement Swapping’ und der Erzeugung von Dreiteilchenverschr¨ankung mithilfe einer gepulsten Quelle f¨ur polarisationsverschr¨ankte Photonen. Mit der Quelle f¨ur Dreiteilchen- verschr¨ankung wurde das erste Experiment zum Test von lokalrealistischen Theorien ohne Ungleichungen durchgef¨uhrt. Die in diesen Experimenten entwickelten Methoden sind von großer Be- deutung f¨ur Forschungen auf dem Gebiet der Quanteninformation und f¨ur zuk¨unftige fundamentale Experimente der Quantenmechanik. 1 Abstract The present thesis is the result of theoretical and experimental work on the physics of multiparticle interference. The theoretical results show that a quantum network with simple quantum logic gates and a handful of qubits enables one to control and manipulate quantum entanglement. Because of the present absence of quantum gate for two independently produced photons, in the mean time we also present a practical way to generate and identify multiparticle entangled state. The experimental work has thoroughly developed the necessary tech- niques to study novel multiparticle interference phenomena. By making use of the pulsed source for polarization entangled photon pairs, in this thesis we report for the first time the experimental realization of quantum teleporta- tion, of entanglement swapping and of production of three-particle entangle- ment. Using the three-particle entanglement source, here we also present the first experimental realization of a test of local realism without inequalities. The methods developed in these experiments are of great significance both for exploring the field of quantum information and for future experiments on the fundamental tests of quantum mechanics. 2 Acknowledgements I am indebted to my advisor, Professor Anton Zeilinger, for his guidance and support throughout the course of my work leading to this thesis. He taught me with wisdom, encouragement, rich knowledge, insight and a deep understanding of physics, and more importantly the way to conduct scientific research. I am very grateful that he has been always available to discuss the many problems and questions I brought him. I would also like to thank him for critically reviewing this thesis. I am very grateful to my second advisor, Professor Helmut Rauch, who warmly recommended and supported my application for the Austrian Chan- cellor Fellowship from the Austrian Academic Exchange Service, which en- abled my continuation of physics study in Austria. I would like to express my deep appreciation to my former and present colleagues in the Quantum Optics and Foundations of Physics research group. Special thanks go to my friend and permanent colleague, Dr. Dik Bouwmeester, who introduced me to the subject of quantum optics and taught me many details of the experiment; he also impressed me with his devotion and ini- tiative. I also especially thank Professor Harald Weinfurter and Matthew Daniell, with whom I collaborated on most of the work. Matthew also has carefully read through some of the chapters in this thesis. Thanks also to the other colleagues in the photon laboratory, Dr. Birgit Dopfer, Dr. Klaus Mattle, Dr. Markus Michler, Dr. Michael Reck, Dr. Surasak Chiangga, Dr. Gregor Weihs, Thomas Jennewein, Alois Mair, Markus Oberparleitner and Christoph Simon. To the people in the atom laboratory, Professor J¨org Schmiedmayer, Dr. Markus Arndt, Dr. Stefan Bernet, Dr. Johannes Den- schlag, Dr. Sonja Frank, Donatella Cassettari, Claudia Keller, Olaf Nairz, and Gerbrand von der Zouw, whose instruments I sometimes stole. And to Mrs. Christine Obmascher, Professor Zeilinger’s secretary, for her quiet effi- ciency in the office, and for her continuous help on various matters throughout 3 the years. Many helpful discussions and much of my knowledge about Bell’s in- equalities are due to my friend and colleague Professor Marek Zukowski, the permanent visitor to our group. Dr. Ramon Risco Delgado and Bjorn Hessmo are always remembered. I enjoyed our discussions about physics, the meaning of life, and all the rest, especially the delicious fish cooked by Bjorn. This work would have been impossible without the patience and under- standing of my wife Xiao-qing, who supported me during the ups and downs that are inevitable in such a major undertaking. My parents have provided me with invaluable support through my entire life and education. They have encouraged and supported me both for starting my undergraduate study in a distant city, and for continuing my doctorate study in another country far away from my homeland. Among the many very good teachers I met throughout my academic ca- reer, I especially thank Professor Yong-de Zhang, my undergraduate and graduate advisor, for his outstanding guidance and continuous concern about my career. I gratefully acknowledge the support of the Austrian Academic Exchange Service during my study. The financial support of the research in this thesis was partially from the Austrian Fonds zur F¨orderung der Wissenschaftlichen Forschung who with the Schwerpunkt Quantenoptik (Project No. S06502), Project No. F1506 and the TMR-Network ”The Physics of Quantum Infor- mation” of the European Commission. The attentive reader might notice that a number of text paragraphs were taken from joint papers of our group because the formulations found there are difficult to improve. Finally I sincerely thank all my friends, from all over the world, who made my years in Innsbruck and Vienna so delightful. Chapter 1 Introduction Superposition, one of the most distinct features of the quantum theory, has been demonstrated in numerous particle analogs of Young’s classic double- slit interference experiment, such as in electron interferometer [Marton et al., 1954], neutron interferometer [Rauch et al., 1974] and atom interferometer [Carnal and Mlynek, 1991; Keith et al., 1991]. However, in multiparticle systems the superposition principle yields phenomena that are much richer and more interesting than anything that can be seen in one-particle systems. Quantum Entanglement, a simple name for superposition in a multipar- ticle system, was first noticed by Schr¨odinger [Schr¨odinger, 1935] and since then it has baffled generations of physicists. It is at the heart of the dis- cussions of the Einstein-Podolsky-Rosen (EPR) paradox, of Bell’s inequality, and of the non-locality of quantum mechanics [Einstein et al., 1935; Bell, 1964]. In recent years, entanglement has become a new focus of activity in quantum physics because of immense theoretical and experimental progress both in the foundation of