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Dissertation DISSERTATION Titel der Dissertation A fundamental test and an application of quantum entanglement angestrebter akademischer Grad Doktor der Naturwissenschaften (Dr. rer.nat.) Verfasserin / Verfasser: Thomas Scheidl Matrikel-Nummer: 9902354 Dissertationsgebiet (lt. Stu- Experimentalphysik dienblatt): Betreuerin / Betreuer: o. Univ.-Prof. Dr. DDr. h. c. Anton Zeilinger Wien, am 19. März 2009 2 Contents 1. Abstract 7 2. Zusammenfassung 9 3. Introduction 11 3.1. Outline of the thesis .............................. 12 4. The basics of photonic qubits 15 4.1. Superposition and Entanglement ....................... 15 4.1.1. Superposition .............................. 15 4.1.2. Entanglement .............................. 15 4.2. Photonic qubits ................................. 16 4.3. No-cloning theorem ............................... 17 4.4. Density matrices ................................ 18 4.5. Measurement .................................. 19 4.6. State tomography ................................ 19 5. Local realism vs. quantum mechanics 21 5.1. EPR’s argument ................................ 22 5.1.1. Bohm version of EPR’s thought experiment ............. 23 5.1.2. Bohr’s response to EPR ........................ 24 5.2. Local realistic theories ............................. 24 5.3. Bell’s theorem .................................. 26 5.3.1. CHSH inequality ............................ 28 5.4. Loopholes .................................... 29 5.4.1. Bell’s assumptions ........................... 29 5.4.2. Locality loophole ............................ 30 5.4.3. Freedom-of-choice loophole ....................... 30 5.4.4. Fair-sampling loophole ......................... 31 5.5. Previous experiments .............................. 32 5.5.1. 1972 - Freedman and Clauser ..................... 32 5.5.2. 1982 - Aspect et al. ........................... 33 5.5.3. 1998 - Weihs et al. ........................... 34 5.5.4. 2001 - Rowe et al. ............................ 36 5.5.5. 2007 - Gr¨oblacher et al. ........................ 36 3 Contents 5.5.6. 2007 - Ursin et al. ............................ 37 6. A Bell test under locality and freedom-of-choice conditions 39 6.1. Required space-time arrangement for the Bell test .............. 40 6.1.1. How to close the locality loophole ................... 40 6.1.2. How to close the freedom-of-choice loophole ............. 43 6.2. Experimental parts ............................... 44 6.2.1. Source of entangled photons ...................... 44 6.2.2. Quantum Random Number Generator ................ 47 6.2.3. Polarization analyzers ......................... 50 6.2.4. Electro-optical modulator ....................... 52 6.2.5. Atmospheric free-space quantum channel ............... 59 6.2.6. Optical fiber channel .......................... 67 6.2.7. Classical channel ............................ 68 6.2.8. Electronics ................................ 69 6.2.9. Time-tagging and coarse synchronization ............... 70 6.2.10. Software and fine synchronization ................... 72 6.3. Experimental situation ............................. 73 6.3.1. Event durations ............................. 74 6.3.2. Final space-time situation ....................... 75 6.4. Measurement procedure ............................ 77 6.4.1. Aligning the Sagnac source ....................... 77 6.4.2. Measuring the attenuation through the quantum channels ..... 78 6.4.3. Establishing a common polarization reference frame ......... 79 6.4.4. Data acquisition ............................. 79 6.5. Results ...................................... 80 6.5.1. Violation of the CHSH inequality ................... 80 6.5.2. State tomography ............................ 83 6.5.3. Different space-time scenarios ..................... 85 6.6. Conclusion and Outlook ............................ 86 7. Quantum cryptography 89 7.1. Coherent state BB84 protocol ......................... 89 7.1.1. Coherent photon states ......................... 89 7.1.2. Protocol ................................. 90 7.1.3. Security ................................. 91 7.2. Entanglement based BB84 protocol ...................... 93 7.2.1. Entangled photon states ........................ 93 7.2.2. Protocol ................................. 93 7.2.3. Security ................................. 94 4 Contents 8. Advantages of entanglement based QKD 95 8.0.4. Theoretical error model ........................ 96 8.1. The experiments ................................ 97 8.1.1. Source at Alice ............................. 99 8.1.2. Source asymmetric in between Alice and Bob ............ 101 8.1.3. Source in the middle .......................... 102 8.1.4. Clock synchronization ......................... 103 8.2. Conclusion and Outlook ............................ 104 A. Preprint 107 B. C++-Code 123 B.1. Source code: coincdosv9.cpp .......................... 123 C. VHDL-Code 133 C.1. Source code: compar.vhd ............................ 133 D. Acknowledgements 147 E. List of Publications 149 F. Curriculum vitae 151 5 Contents 6 1. Abstract This work describes two experiments that are based on correlation measurements between entangled photons, spatially separated by 144 km between the Canary Islands, La Palma and Tenerife. The first of which contributes to the debate of whether or not quantum mechanical predictions can be described within a local realistic frame, a question that plays a fun- damental role in the foundation of quantum mechanics ever since the famous Einstein- Podolsky-Rosen (EPR) “paradox” [1]. The experiment presented is a test of the CHSH form [2] of Bell’s inequality [3], simultaneously closing two out of three possible “loop- holes” for local realism that can arise in an experimental Bell test. These two loopholes are the locality loophole and the freedom-of-choice loophole. The latter has not been addressed experimentally so far and was closed for the first time in our experiment by space-like separating the setting choice from the photon pair emission. Unfortunately, the third crucial loophole, i.e., the fair-sampling loophole [4], could not be closed due to inefficient photon detection. However, our experiment is the first to close more than one loophole at a time. By violating the CHSH inequality by more than 16 standard deviations with Sexp = 2.37 ± 0.023, this is the most conclusive violation of local realism to date and represents an important step towards a completely loophole-free Bell test, which is one of the most significant still-unresolved challenges in fundamental physics. Within the second experiment described, the intriguing properties of photonic entan- glement are exploited for demonstrating entanglement based quantum key distribution (QKD), probably one of the most mature applications in the field of quantum informa- tion and quantum communication. In high loss situations, such as in the case of future satellite based or optical fiber based quantum communication networks, it is important to implement the most efficient experimental QKD scheme. It has recently been empha- sized [5] that entanglement based quantum key distribution systems can tolerate higher channel losses compared to systems based on weak coherent laser pulses. This is in par- ticular the case when the entangled photon source is located symmetrically between the two receiver stations, called Alice and Bob. We experimentally studied this important advantage by implementing different entanglement based QKD setups on a 144 km free- space link between the two Canary Islands, La Palma and Tenerife. We studied three different configurations that operated at two-photon attenuations of 35 dB, 58 dB and 71 dB, respectively. In these experiments, the entangled photon source was placed either at Alice’s location, asymmetrically between Alice and Bob or symmetrically in the middle between Alice and Bob. In addition, we show that our experimental results agree well with the theoretical model devised in [5], which we applied to our experimental param- eters. Compared to the expected link attenuations in a low-earth-orbit (LEO) satellite to ground scenario [6], as it might be implemented in a future network, we expect from 7 1. Abstract our results that entanglement based QKD systems are suitable to be used within either a single-downlink configuration or a configuration with two simultaneous downlinks [7]. 8 2. Zusammenfassung Diese Arbeit beschreibt zwei Experimente, die auf Korrelationsmessungen zwischen ver- schr¨ankten Photonen basieren. Die Photonen werden dabei zwischen den kanarischen Inseln La Palma und Teneriffa 144 km r¨aumlich voneinander getrennt. Das erste Experiment tr¨agtzur Diskussion dar¨uber bei, ob quantenmechanische Vorher- sagen innerhalb eines lokal-realistischen Rahmens beschrieben werden k¨onnen. Diese Frage spielt seit der Ver¨offentlichung des ber¨uhmten Einstein-Podolsky-Rosen “Para- doxons” [1] eine fundamentale Rolle in der Begr¨undungder Quantenmechanik. Das beschriebene Experiment ist ein Test der CHSH Form [2] der Bell’schen Ungleichung [3] und schließt gleichzeitig zwei der drei “Schlupfl¨ocher” f¨urlokalen Realismus, die in einem experimentellen Test der Bell’schen Ungleichung auftreten k¨onnen.Es sind dies das Lo- cality und das Freedom-of-choice Schlupfloch. Letzteres wurde bis heute experimentell nicht adressiert und zu allererst in unserem Experiment durch raumzeitliche Trennung der Wahl der Analysatorstellung und der Photonemission geschlossen. Das dritte Schlupfloch, das Fair-sampling Schlupfloch [4], konnte wegen zu niedriger Detektionseffizienz leider nicht
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