Frontiers of Quantum Optics: photonics tolls, computational complexity, quantum metrology, and quantum correlations. Raphael Akel Abrahao˜ M. Eng. A thesis submitted for the degree of Doctor of Philosophy at The University of Queensland in 2020 School of Mathematics and Physics Abstract The concept that light comes in discrete units of energy, the quantum of light named photon, is a cornerstone of Quantum Physics. Current technology allow experimentalists to generate, manipulate and detect photons in ways only imaginable for the earlier formulators of Quantum Physics. Nowadays, we can use photons to test fundamental aspects of Quantum Physics, as well as to develop applications, specially in the fields of quantum computation, communication, cryptography, metrology and sensing. This thesis aims to explore the frontiers of Quantum Optics in 4 fronts: (1) quantum photonics tools, (2) quantum computing and computational complexity, (3) quantum metrology, and (4) quantum correlations. The research presented here can be formulated in 4 respective questions: How to prepare a state with a large number of single photons? • Using our Multiple Channel Optical Switcher photonic chip. How to scale Boson Sampling experiments, specially to a regime where it is closer to the • quantum computational advantage and/or can challenge the Extended Church-Turing Thesis? Combining continuous-variables optical technology with temporal encoding. How to demonstrate an optimal method to estimate the spacial characteristics of a distant source • of thermal light? Using recent advances in quantum metrology and number-resolving photon detectors. Are there quantum correlations beyond entanglement and discord? • Probably yes. Of course, even to better understand what each of these questions and answers mean, it is necessary a minimum background which I tried to provide in the beginning of the thesis and in each chapter. The reader will find out the details of each of these questions and answers. I wish you a good reading! Declaration by author This thesis is composed of my original work, and contains no material previously published or written by another person except where due reference has been made in the text. I have clearly stated the contribution by others to jointly-authored works that I have included in my thesis. I have clearly stated the contribution of others to my thesis as a whole, including statistical assistance, survey design, data analysis, significant technical procedures, professional editorial advice, financial support and any other original research work used or reported in my thesis. The content of my thesis is the result of work I have carried out since the commencement of my higher degree by research candidature and does not include a substantial part of work that has been submitted to qualify for the award of any other degree or diploma in any university or other tertiary institution. I have clearly stated which parts of my thesis, if any, have been submitted to qualify for another award. I acknowledge that an electronic copy of my thesis must be lodged with the University Library and, subject to the policy and procedures of The University of Queensland, the thesis be made available for research and study in accordance with the Copyright Act 1968 unless a period of embargo has been approved by the Dean of the Graduate School. I acknowledge that copyright of all material contained in my thesis resides with the copyright holder(s) of that material. Where appropriate I have obtained copyright permission from the copyright holder to reproduce material in this thesis and have sought permission from co-authors for any jointly authored works included in the thesis. Publications included in this thesis 1. [1] F. Lenzini, B. Haylock, J. C. Loredo, R. A. Abrahao˜ , N. A. Zakaria, S. Kasture, I. Sagnes, A. Lemaitre, H.-P. Phan, D. V. Dao, P. Senellart, M. P. Almeida, A. G. White, and M. Lobino, Active demultiplexing of single photons from a solid-state source, Laser Photonics Reviews 11, No. 3, 1600297, 2017. 2. [2] L. A. Howard, G. G. Gillett, M. E. Pearce, R. A. Abrahao, T. J. Weinhold, P. Kok, A. G. White, Optimal imaging of remote bodies using quantum detectors, Physical Review Letters 123, 143604, 2019. Submitted manuscripts included in this thesis 1. [3] Raphael A. Abrahao and Austin P. Lund, Continuous-Variables Boson Sampling: Scaling and Verification, arXiv:1812.08978, 2018. Other publications during candidature Conference abstracts 1. R. A. Abrahao,˜ F. Shahandeh, G. Gillet, M. Ringbauer, M. P. Almeida, T. C. Ralph and A. G. White, “The Quest for Nonclassicality using Number-Resolving Single-Photon Detectors”, in Australian and New Zealand Conference on Optics and Photonics (ANZCOP) 2017, Queenstown, New Zealand. 2. [4] R. A. Abrahao,˜ F. Shahandeh, G. Gillett, M. Ringbauer, T. Weinhold, M. P. Almeida, T. C. Ralph, and A. G. White, “The Quest for Nonclassicality using Number-Resolving Single-Photon Detectors”, in Frontiers in Optics / Laser Science, OSA Technical Digest (Optical Society of America, 2018), paper JTu2A.55. Contributions by others to the thesis Before Chapters 2, 3, 4 and 5, the contributions of each author for each project are stated. Statement of parts of the thesis submitted to qualify for the award of another degree No works submitted towards another degree have been included in this thesis. Research involving human or animal subjects No animal or human subjects were involved in this research. Acknowledgments I would like to sincerely thank my PhD Advisory team: Prof. Andrew White, Dr Till Weinhold, Dr Austin Lund, and Dr Martin Ringbauer. In particular, without limiting to, I would like to thank Prof. Andrew White for the opportunity to study on the Quantum Technology Laboratory (QT Lab) and for the encouragement to take different projects; Dr Till Weinhold for many assistances in different parts of my PhD, from technical questions in the lab to general candidature help; Dr Austin Lund for his help on theoretical physics (and the best Quantum Physics discussion in a beachfront bar); and Dr Martin Ringbauer for pointing me in the direction of quantum foundations, a truly deep influence. Certainly was a special time of my life. My heartfelt gratitude! I would like to extend my gratitude to Dr Marcelo de Almeida, specially for his help during my first year, Dr Jacquiline Romero and all my fellow PhD students in the QT Lab. Additionally, I would like to thank Dr Magdalena Zych for the many interesting discussions about General Relativity and Quantum Physics. Also, I would like to thank all the people that contributed to the projects presented in this thesis. This PhD was immensely facilitated by the extraordinary work of many University of Queensland staffs, especially Angela Bird, Murray Kane, Jonathan Paul, and Dr Timo Nieminen. I also would like to thank Dr Nathan Langford, who provided me encouragement, advice and support though the EQUS Mentorship Program. Muito obrigado! Financial support This research was supported by the University of Queensland International Scholarship (UQI), Aus- tralian Research Council Centre of Excellence for Engineered Quantum Systems (EQUS), and Aus- tralian Research Council Centre of Excellence for Quantum Computation and Communication Tech- nology (CQC2T). Keywords Quantum Physics, optics, metrology, correlations, photonics, computational complexity. Australian and New Zealand Standard Research Classifications (ANZSRC) ANZSRC code: 020604, Quantum Optics, 100% Fields of Research (FoR) Classification FoR code: 0206, Quantum Physics, 100% To God To Amanda Akel Abrahao,˜ in memoriam To Mario Isaac Abrahao,˜ in memoriam To Constantino Nicolau Akel, in memoriam To my beloved wife, Renata To my beloved children, Mario, Amanda and Miguel To my beloved father and mother, Sergio and Irlane To my beloved grandmothers, Lily and Irene To my siblings, Gabriel and Mariana Sacred Heart of Jesus, in whom are all treasures of wisdom and knowledge, have mercy on us. Immaculate Heart of Mary, pray for us. Saint Joseph, pray for us. Contents Abstract . ii Contents ix List of figures xii List of tables xv 1 Fundamentals of Single-Photon Sources 3 1.1 What is a photon? . 3 1.1.1 Properties of photons . 4 1.2 Metrics of single-photon sources . 4 1.2.1 Photon number purity (a.k.a single-photon purity or multiphoton suppression) 5 1.2.2 Indistinguishability . 10 1.2.3 Brightness . 13 1.2.4 Nomenclature: manifold single photons vs multiphotons . 13 1.3 Single-photon sources . 13 1.3.1 Quantum Dots: solid-state single-photon sources . 14 1.3.2 Quantum nonlinear sources . 16 1.4 Entangled states . 18 2 Multiple Channel Optical Switcher (MuChOS) 23 2.1 The need for manifold single photons . 24 2.2 Demultiplexing Photons from a Quantum Dot . 24 2.3 Passive Demultiplexing . 26 2.4 Active Demultiplexing using Pockels cell or Electro-Optic Modulator (EOM) . 26 2.5 Active Demultiplexing with Integrated Photonics . 27 2.5.1 Scaling of single-photon demultiplexing using MuChOS . 29 2.5.2 Fabrication of MuChOS . 29 2.5.3 Performance of MuChOS . 31 2.6 Conclusion . 34 ix x CONTENTS 3 Continuous-Variables Boson Sampling: Scaling and Verification 37 3.1 Introduction . 37 3.2 A glimpse into Computational Complexity . 37 3.2.1 Computational Complexity Classes . 38 3.2.2 Polynomial Hierarchy . 39 3.3 Introduction to Boson Sampling . 41 3.4 Implementations of Boson Sampling . 43 3.5 Applications of Boson Sampling . 45 3.6 The problem: the current status of Boson Sampling . 45 3.7 The proposed solution: combining continuous-variables Boson Sampling with temporal encoding . 47 3.8 Continuous-Variables Boson Sampling: Verification . 50 3.9 Continuous-Variables Boson Sampling: Sampling . 50 3.10 The role of imperfections . 51 3.11 Conclusion . 52 4 Optimal Imaging of Remote Bodies using Quantum Detectors 55 4.1 Introduction . 55 4.2 Optimal Imaging of Remote Bodies: Methods . 57 4.2.1 Source size and angle estimation .