Geometrical and Topological Aspects of Quantum Information Systems By Tommaso Federico Demarie arXiv:1407.6152v1 [quant-ph] 23 Jul 2014 A thesis submitted to Macquarie University for the degree of Doctor of Philosophy Department of Physics and Astronomy December 2013 ii c Tommaso Federico Demarie, 2018. Typeset in LATEX 2". iii Except where acknowledged in the customary manner, the material presented in this thesis is, to the best of my knowledge, original and has not been submitted in whole or part for a degree in any University. Tommaso Federico Demarie iv \Another uninnocent elegant fall into the unmagnificent lives of adults." The National - Mistaken for Strangers Acknowledgements Since the censoring red pen of my supervisor Danny does not have access to the Ac- knowledgments, here I am allowed to be as poetical and flowery as I like. Ergo forgive me if, more often than I should, I will fall off the cliff of scientific standards. First of all I sincerely need to express my gratitude to all the people who told me that moving to Australia was to stupidest idea ever. I am glad you have been hon- est, and I am glad I did not listen to you. And thank you Eva for letting me go, after all. The biggest thank you goes to the two people who offered (and gave) me the chance of being here, my supervisors A/Prof. Daniel Terno and A/Prof. Gavin Brennen. Danny, you have been a great boss. Thanks from the bottom of my heart for the support you provided me during these years. Apart from being a passionate and amaz- ing physicist, you pushed me to find my own ways, encouraged me to explore new ideas and gave me space to work on what I liked the most. I am sure that more than once you would have loved to put your hands around my neck and firmly close your fingers, but you never did it. In fact, you have always been ready to help me when in need, to kick me when lazy and to congratulate me those few times I did some- thing good. From you I learnt to love the rigor in working and not to fear taking the wrong way (for a short while) when researching. And if I was the only freak in the office who got excited about foundations, that is definitely your fault. Thanks for everything! Gavin, thanks for being always patient and available to explain again, and again, and again, anything I would not feel confident about. I have always been impressed by the apparently unlimited extension of your knowledge about any concept in Physics. It was easy to see how much passion you put in your work and this motivated me to improve and do my best all the time. Thanks also for sending me around the world. It has been a real privilege working and partying with you! Along the duration of my studies I have met some great people, whom I have been fortunate enough to work with. Let me say few words about them. v vi Acknowledgements To start, I would like to thank Prof. Kwek for inviting me to visit his group in Singapore and taking me to eat any sort of delicious food while discussing great physics. And I am equally grateful to Prof. Murao for inviting me to pay a visit to her group in Tokyo. It is also my pleasure to thank Dr. Sai Vinjanampathy for the great time spent together at CQT and in the various Hawker centers of Singapore. Witnessing our discussions shifting from Star Trek to warp drive in general relativity was a clear manifestation of the beauty of being nerds. Equally kind has been Michal Hajdusek, who organized my visit to Tokyo, providing me with financial support: Dude, it was great talking physics, but it was even greater lowering the already pretty low level of the Celt one beer after the other. You guys are legends! Nicolas "Doc" Menicucci, you have been an example both at the whiteboard and on the dance floor. Doing calculations via Skype at 4 a.m. with you is something that, one day, I will proudly tell my kids. You taught me the importance of perfection and I will always keep in mind your lesson: It makes no sense to upload it on the arxiv if it is not going to be the best paper out there. And needless to say, thanks for sharing your best pick-up lines with me. A warm thank you to all the admin people who constantly helped me fixing any sort of bureaucratic trouble. Especially Lisa: It is a miracle that you never threw something at me after the n-th time I would give you again the wrong module. Also thanks to Michele for her constant (and patient) help with tickets and flights! There are some special people I wish to thank: They are Aharon the Dude, An- drea and Hossein, Cristina culo gordo, Franceschina, Eleonora la Dude, Luchino and Marion, Mauro il Dude, Paolino, His darkness Saatana and Thorn. You have been like brothers and sisters to me. I always knew that, no matter what, with you guys around I would have been safe and sound. Together we shared so much foolery, laughters, sometimes tears, and I am extremely grateful to all of you guys for that. Allow me to be particularly sentimental: Aharon, thanks for your friendship (in the shape of suggestions, bad jokes, physics, coffee, beer and food). It always soothed the mess that distance and uncertainty sometimes caused in my mind. Franceschina, I know that although you expressed disgust any time I hugged you too tight, you liked every bit of it. Thanks for offering me a roof and a cot when I needed it the most! Mauro, it has been phenomenal making this journey together. We have shared too much beer, meat and mead to tell it all here in a few lines. Good luck with the rest of the adventure, and hold me a dry spot under the bridge please. vii Everybody knows about the tragedy of finding a proper house in Australia1. How- ever, in these years I have been extremely lucky to share low standards of living and poor hygienic conditions with some amazing characters, who undoubtedly made the whole experience of living in Sydney more special. Therefore, let me thank Safi, Josh, Kamin, Gabriela and especially Marika, who took care of me like a younger brother. And a special tribute goes to Lili, who helped me to overcome my dislike of cats. I should ideally thank so many more people for too many reasons. Anyone I met in the last years gave me something special and in a way made me the person I am to- day. However, allow me to name \few" of these beings who are particularly important to me: Alika, ChrisMcMahon, Christoph, Doozie, Enzo, Federica, Geraldine, Helena, Ivan, Jacopo, Johann and Elna, Kayla and Xavier, Michael and Louise, Nieke, Nora and Jack, Richard and Marija, Robert, Sukhi, Valentina A, Valentina B, Valentina D, Vikesh, and the rest of the quantum guys. Thanks folks for being part of this adventure. Thanks to my friends in Italy who have never forgotten me while I have been away and have always forgiven my unjustifiable long pauses in replying to emails and phone calls: I hug you all Alberto, Castagna, Chiara, Damiano, Elena B, Elena G, Eleonora, Francesco and Lucia, Gianni, Giulia, the Goitre, Lara, and Stefania. Every time I visit the Bacic family in Brisbane and the Aso family in Tokyo I feel welcomed like a son, and it is an amazing feeling indeed. I thank you for your generos- ity! Knowing that I have an extended family across the borders of this planet is like sweet popcorn for my soul. Thank you Orly, for both the great and the disastrous time spent together. You taught me the value of honesty and integrity the hard way and I shall not forget it. It is people like Ai Leen that make the world shivering with hope. Thanks for being so caring, idealistic and never ready to compromise. You are a wonderful small little being, please promise me you will never change, no matter what. Thanks Sabrina for making these last months here in Sydney special. I could have easily drowned into the deep sea of despair, but you managed to hold me up with a strong grasp and an enchanting smile. Some things happen unexpectedly, and you surely are a surprising but wonderful gift. Last, but certainly not least, I wish to thank my family, for all the support and unconditional love you gave me in these years. My mum, Federica, who won her fears and flew all the way down under to see with her own eyes the places I have been telling 1If you do not, well, read \He died with a falafel in his hand" by J. Birmingham. viii Acknowledgements her about. My dad, Gianpiero, who will be ecstatic to have my burden back on his shoulders. Nonna Irma, who innocently asked me how long it takes to get to Sydney by train. Thanks also to my brother Alessandro, my aunties Renata and Chiara and my cousins. A thought always goes to my grandparents who are not here anymore: Nonno Beppe, Nonna Nella and Nonno Severino, I know how proud you are that your fool of a grandson made it to the end. I dedicate this work to you. \Considerate la vostra semenza: fatti non foste a viver come bruti, ma per seguir virtute e canoscenza." Dante Alighieri - Inferno, Canto XXVI List of Publications [1] A.