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Photonic Multipartite Entanglement Massimiliano Smania Photonic multipartite entanglement Generation, measurement and applications Photonic multipartite entanglement Photonic multipartite Massimiliano Smania Massimiliano Smania received his BSc and MSc degrees in Physics from the University of Padua. His Master's thesis on quantum communication was carried out at Stockholm University, where he also completed his PhD in Physics. ISBN 978-91-7911-030-7 Department of Physics Doctoral Thesis in Physics at Stockholm University, Sweden 2020 Photonic multipartite entanglement Generation, measurement and applications Massimiliano Smania Academic dissertation for the Degree of Doctor of Philosophy in Physics at Stockholm University to be publicly defended on Thursday 10 September 2020 at 09.00 in FB41, AlbaNova universitetscentrum, Roslagstullsbacken 21, digitally via conference (Zoom), public link https:// stockholmuniversity.zoom.us/s/239996391. Abstract We are currently witnessing a fundamental change in the field of quantum information, whereby protocols and experiments previously performed in university labs are now being implemented in real-world scenarios, and a strong commercial push for new and reliable applications is contributing significantly in advancing fundamental research. In this thesis and related included papers, I first look at a keystone of quantum science, Bell's theorem. In particular, I will expose an issue that we call apparent signalling, which affects many current and past experiments relying on Bell tests. A statistical test of the impact of apparent signalling is described, together with experimental approaches to successfully mitigate it. Next, I consider one of the most refined ideas that recently emerged in quantum information, device-independent certification. Device-independent quantum information aims at answering the question: "Assuming we trust quantum mechanics, what can we conclude about the quantum systems or the measurement operators in a given experiment, based solely on its results, while making minimal assumptions on the physical devices used?". In my work, the problem was successfully approached in two different scenarios, one based on entangled photons and the other on prepare-and-measure experiments with single photons, with the aim of certifying informationally-complete quantum measurements. Finally, I conclude by presenting an elegant and promising approach to the experimental generation of multi-photon entanglement, which is a fundamental prerequisite in most modern quantum information protocols. Keywords: quantum information, entanglement, Bell tests, POVM, device-independent, self-testing, quantum optics, prepare-and-measure. Stockholm 2020 http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-182523 ISBN 978-91-7911-030-7 ISBN 978-91-7911-031-4 Department of Physics Stockholm University, 106 91 Stockholm PHOTONIC MULTIPARTITE ENTANGLEMENT Massimiliano Smania Photonic multipartite entanglement Generation, measurement and applications Massimiliano Smania ©Massimiliano Smania, Stockholm University 2020 ISBN print 978-91-7911-030-7 ISBN PDF 978-91-7911-031-4 Thesis for the degree of Doctor of Philosophy in Physics Department of Physics, Stockholm University, Sweden. ©Paper II: 2020 Optical Society of America. ©Paper III: 2020 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY- NC). Typeset by the author using LaTeX. Based on Harish Bhanderi's PhD/MPhil template, available at: http://www-h.eng.cam.ac.uk/help/tpl/textprocessing/ThesisStyle/. Corrected and extended in 2007 by Jakob Suckale, and made available through OpenWetWare.org. Modified for SU by Andreas Solders in 2011. Additional bug fixes and made available on GitHub by Samuel Bohman in 2017. Printed in Sweden by Universitetsservice US-AB, Stockholm 2020 Distributor: Department of Physics, Stockholm University To my parents. Ai miei genitori. Abstract We are currently witnessing a fundamental change in the field of quantum information, whereby protocols and experiments previously performed in university labs are now being implemented in real-world scenarios, and a strong commercial push for new and reliable applications is contributing significantly in advancing fundamental research. In this thesis and related included papers, I first look at a keystone of quantum science, Bell’s theo- rem. In particular, I will expose an issue that we call apparent signalling, which affects many current and past experiments relying on Bell tests. A statistical test of the impact of apparent signalling is described, together with experimental approaches to successfully mitigate it. Next, I consider one of the most refined ideas that recently emerged in quantum information, device-independent certification. Device-independent quantum information aims at answering the question: “Assuming we trust quantum mechanics, what can we conclude about the quantum systems or the measurement op- erators in a given experiment, based solely on its results, while making min- imal assumptions on the physical devices used?”. In my work, the problem was successfully approached in two different scenarios, one based on entan- gled photons and the other on prepare-and-measure experiments with sin- gle photons, with the aim of certifying informationally-complete quantum measurements. Finally, I conclude by presenting an elegant and promis- ing approach to the experimental generation of multi-photon entanglement, which is a fundamental prerequisite in most modern quantum information protocols. v vi Acknowledgements It is not a coincidence that most acknowledgement sections in dissertations begin with the doctoral supervisor. My PhD would not have been possible without the scientific, moral and financial support of Mohamed Bouren- nane. I especially thank you for all our never-ending discussions on the most diverse topics, which, besides keeping me from supper, have in time come to constitute the foundations of some of the skills I have developed outside of the scientific realm in the past few years. I also thank my co-supervisor Markus Hennrich, for always being knowl- edgeable and clear whenever explaining complex quantum optics concepts to me, and Per-Erik Tegner for his guidance and help as a doctoral mentor. Ingemar Bengtsson, your generosity and dedication in helping students are lights in the sometimes dark corridors of Academia, and have proven useful multiple times in my path. Five years are a rather long time in academic terms, which is why I had the chance to meet and collaborate with several researchers without whom this work would have never reached a satisfactory end. Among them, I would like to thank Ashraf, Sadiq, Hammad and Nawareg, who shared with me countless hours of work and discussion inside and outside the lab. I am also grateful to my co-authors Adán, Matthias, Piotr and Armin. There would be no papers in this thesis without you. My experience in research so far has also been invaluably enhanced by the strong sense of community I felt in my everyday work, especially among fellow students. I thank Marco, Alley, Walid, Natalie, Alban, Alexander, Gerard, Fabian, Irina, Pil, and each and every person in the KIKO group. My time in Albanova would have been miserable without all of you. Unlike my Masters thesis, these acknowledgements will be part of the final printed version, thus I have to resist switching to more emotional southern languages. Ornella and Franco, although I have never had the chance to try other parents, I am absolutely and scientifically certain that you are the best in the world. You and my brother are the ground I walk on and the sky I look up to. Thank you. Nicola, thank you also for the ever-too-brief times spent together in these few years. The distance that separates us is but a number, and if this goes to plan, I will soon achieve total control over numbers. This section of my acknowledgements would vii not be complete without the latest addition to my family: Vani, the efforts and sacrifices you made so I could reach this goal are what made it worth in the first place. Thank you for taking care of me as if your life depended on it, your attention is what kept me going. Karin and Paolo, thank you for being the best friends to live next to in a pandemic, and so much more. Actually, thank you Karin for the Sam- manfattning too, for giving me a place to sleep, for covering my rent when I could not pay, for sharing apartments with me throughout my PhD, and additional crucial help which would need a separate section just to list. Thank you Andrea for exchanging doubts on our aptitude as researchers, and for long and intricate discussions on all of the big themes in the world. Both made us stronger. I am also grateful to all the friends that have made my time outside Albanova so much fun, in particular the Desert Island team and the ever-expanding Italian club. Sincere thanks also to all the friends who, although not in Stockholm, played a fundamental role during the time of my PhD studies anyway. In particular, I would like to thank Davide, Luca, Alice, Ale, Ale, Degia, Joey, Danel and Tri. Your friendship has time and again proven stronger than the distance that divides us. Last but not least, the research work carried out in this thesis was funded by the Knut and Alice Wallenberg Foundation and the Swedish Research Council. viii Contents Abstract v Acknowledgements vii List of Papers xii Author’s contribution xiii Relevant papers not included in the thesis xiv List of Figures xv List of Tables xvii Sammanfattning xviii Preface xix 1 Bits of quantum information 1 1.1 The qubit . .1 1.2 Multi-qubit systems . .2 1.3 Mixed states . .4 1.4 Quantum measurements . .5 1.4.1 Projective measurements . .6 1.4.2 Generalised measurements . .7 1.4.3 SIC-POVM . .8 1.4.4 Trine-POVM . .9 1.5 Quantum state fidelity . 10 1.6 Entanglement . 10 1.6.1 Entanglement witness . 11 1.7 Bell states . 12 ix 2 Bell tests 13 2.1 The EPR paradox .
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