AGILE QUANTUM CRYPTOGRAPHY AND NON-CLASSICAL STATE GENERATION Matthew Thornton A Thesis Submitted for the Degree of PhD at the University of St Andrews 2020 Full metadata for this item is available in St Andrews Research Repository at: http://research-repository.st-andrews.ac.uk/ Please use this identifier to cite or link to this item: http://hdl.handle.net/10023/21361 This item is protected by original copyright Agile quantum cryptography and non-classical state generation Matthew Thornton This thesis is submitted in partial fulfilment for the degree of Doctor of Philosophy (PhD) at the University of St Andrews March 2020 PUBLICATIONS The following publications have resulted from the research contained in this Thesis: M. Thornton, H. Scott, C. Croal and N. Korolkova: Continuous-variable quantum digital signatures over insecure quantum channels, Physical Review A 99, 032341, (2019). M. Thornton, A. Sakovich, A. Mikhalychev, J. D. Ferrer, P. de la Hoz, N. Korolkova and D. Mogilevtsev: Coherent diffusive photon gun for generating nonclassical states, Physical Review Applied 12, 064051, (2019). S. Richter, M. Thornton, I. Khan, H. Scott, K. Jaksch, U. Vogl, B. Stiller, G. Leuchs, C. Marquardt and N. Korolkova: Agile quantum communication: signatures and secrets, arXiv:2001.10089 [quant-ph]. v CONFERENCEPRESENTATIONS I have had the privilege to present at the following conferences: 1. QCrypt 2016, Washington DC, USA. Poster presentation: “Con- tinuous variable quantum digital signatures.” 2. 6th International Conference on New Frontiers in Physics (ICNFP 2017), Kolymbari, Crete. Oral presentation: “Gigahertz quantum signatures compatible with telecommunication technologies.” 3. QCrypt 2017, Cambridge, UK. Poster presentation: “Gigahertz quantum signatures compatible with telecommunication tech- nologies.” 4. WE-Heraeus-Seminar on “Quantum Correlations in Space and Time,” 2017, Bad Honnef, Germany. Poster presentation: “Giga- hertz quantum signatures compatible with telecommunication technologies.” 5. 25th Central European Workshop on Quantum Optics (CEWQO 2018), Palma de Mallorca, Spain. Poster presentation: “Giga- hertz quantum signatures compatible with telecommunication technologies.” 6. 24th Young Atom Opticians (YAO 2018), Glasgow, Scotland. Poster presentation: “Coherent quantum networks for non-classical state generation.” 7. Quantum Roundabout 2018, Nottingham, UK. Poster presenta- tion: “Efficient generation of sub-Poissonian light via coherent diffusive photonics.” 8. 1st European Quantum Technologies Conference (EQTC 2019), Grenoble, France. Poster presentation: “Efficient generation of sub-Poissonian light via coherent diffusive photonics.” 9. ICQOQI 2019, Minsk, Belarus. Oral presentation: “Continuous- variable quantum digital signatures over insecure channels.” 10. Quantum Information Scotland (QUISCO) September 2019, St Andrews, Scotland. Oral presentation: “Agile quantum commu- nication: quantum signatures and quantum secrets.” vii COLLABORATIONSTATEMENT This Thesis is the result of work which I carried out at the University of St Andrews between September 2016 and March 2020. Much of the work contained here has been published in (or submitted to) refereed scientific journals. All text in this Thesis has been written entirely by me. Unless otherwise stated, all figures have been created entirely by me. Content in Chapter 3 and AppendixC is also contained in M. Thornton et. al., Phys. Rev. A 99, 032341 (2019). Theoretical work was conducted in collaboration with H. Scott. All numerics used to generate results and figures in Ch. 3 were created by me. Chapters 4 and 5 are extensions of work contained in S. Richter et. al., arXiv:2001.10089 [quant-ph]. The original ideas and framework underpinning Ch. 5 were formulated during discussions I partook in at the Max-Planck-Institute für die Physik des Lichts (MPL) in Erlangen, Germany in May 2017. The work was completed in collaboration with S. Richter, I. Khan and C. Marquardt. My contribution was the theoretical analysis and security proofs which underpin the chapters, while the experiment discussed in Sec. 5.5 was performed at MPL by S. Richter and I. Khan, with assistance from K. Jaksch, U. Vogl, B. Stiller, G. Leuchs and C. Marquardt. I analysed experimental data with additional assistance from S. Richter and I. Khan. Chapter 6 is an expansion on content contained in M. Thornton et. al., Phys. Rev. Applied 12, 064051,(2019). N. Korolkova and D. Mogilevtsev provided the direction and original ideas for the work. The work contained in Ch. 6 was carried out by myself in collaboration with D. Mogilevtsev and P. de la Hoz, and with assistance from A. Sakovich for the numerics. All work in this Thesis has been supported by my supervisor, Pro- fessor N. Korolkova. ix THESISABSTRACT In the first half of this Thesis, we introduce a framework of “quantum cryptographic agility,” which allows for a resource-efficient swap of an underlying cryptographic protocol. Specifically, we introduce several schemes which perform the tasks of Digital Signatures and Secret Sharing. Our first achievement is an investigation of Quantum Digital Signatures (QDS) over a continuous-variables platform, consisting of phase-encoded coherent states and heterodyne phase detection. QDS allows for secure authentication of a classical message, while guaranteeing message transferability. For the first time, we prove security of CV QDS in the presence of an eavesdropper on the quantum channels. We then introduce a continuous variable (CV) Quantum Secret Sharing (QSS) protocol. Our security proof allows for classical infor- mation to be split and shared between multiple potentially dishonest recipients, while retaining security against collective beamsplitter and entangling-cloner attacks. In the last chapter of this half, we introduce another QDS scheme which runs over identical hardware setup to our QSS protocol. We analyse experimental data in which quantum coherent states were distributed at a rate of 1 GHz, which for QDS allows us to securely sign a message in less than 0.05 ms. In the second half of this Thesis we suggest and discuss a determin- istic source of nonclassical light, which we call “PhoG”. Our source is based on the coherent diffusive photonics, relying on both coherent and dissipative evolution of the quantum state, and may be realised in an array of dissipatively-coupled laser-inscribed waveguides in a χ(3) glass. We analyse the PhoG device with several analytical and numerical models and demonstrate that a coherent state input leads to a bright output state with strong photon-number squeezing. With minor reconfiguration our system can generate entangelement be- tween spatially separated modes via a process analogous to four-wave mixing. xi General acknowledgements I would like to first thank my supervisor, Professor Natalia Korolkova, for her support and help over the past four years. My PhD has been fun, long, thrilling, difficult, enjoyable, frustrating, brilliant and always sinusoidal, and I am grateful to Natalia for her guidance and help in navigating each of these aspects. I should thank the many colleagues (and now friends) within the School of Physics and Astronomy who have contributed fun conversation and probing questions, and who have helped make the last four years so much fun. I have deeply appreciated these opportunities to grow in self-management and self-leadership, in scientific ability, in public speaking, in teaching, in writing, and in understanding and appreciation for our wonderful universe. Thank you to every undergraduate student I have taught or interacted with - you have reminded me that “yes I actually do quite enjoy physics, let me tell you why”. Thanks, Anton, for helping me understand Mathematica and Git. Thank you also to Hamish, to Jesús and to Cailean for giving me the privilege to work with you and explore fun aspects of quantum physics. I enjoyed it and I hope you did too. I acknowledge deep support from my family. Thanks for listening to me trying to explain my research time and time again, and thanks especially to my parents for instilling in me a love and an appreciation for science and mathematics. I am grateful to Dad for convincing me to pursue physics (instead of Chemistry), and to both Mum and Dad for working so hard to support me financially through my first degree, and emotionally during this one. And thanks to my siblings Peter, Naomi, Annalise, Abigail and Andy for many years of friendship and encouragement. I could not have survived without a little help from my friends. I am grateful, in particular, to those at St Andrews Baptist Church, who have put up with my potent combination of too-little-sleep and too-much-coffee for the last nine years. You have reminded me that there are bigger things to focus on and enjoy than the PhD, and more important places to find my self-worth and satisfaction than in my own productivity and scientific output. Thank you to Jesus for making (quantum) light in the first place. Thanks to everyone in the “Commune”. Thanks especially to James and Belinda, David, Daffyd, Jordan and Tamara, Emily, Gavin, the Milkman, the Irregulars, and so many more. I should say “thank you” to Andrew Rollinson for encouraging me towards a PhD in the first place (though he's probably forgotten about it) and say “hello” to Jason Isaacs. Finally, I am deeply indebted for the love and support I have received from my wife Hannah. She has encouraged me when the PhD has just been plain annoying and rejoiced with me when it has just been plain