The emergence of objectivity and the quantum-to-classical transition Thao Phuong Le A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy of University College London Department of Physics and Astronomy University College London November 2020 I, Thao Phuong Le confirm that the work presented in this thesis is my own. Where information has been derived from other sources, I confirm that this has been indicated in the thesis. Signature .................................................. Date ............................. Abstract Quantum mechanics describes the smallest systems, whilst classical physics de- scribes macroscopic scales. However, the quantum-to-classical transition is a major unsolved problem. In this thesis, we develop further understanding of the transition through the concept of objectivity. The objects we perceive in our everyday world are objective: they exist regardless of observation, and their properties are independent of observers. Quantum Darwinism is a conceptual and theoretical framework that describes the emergence of objectivity. The thesis addresses the quantitative description of objectivity, the dynam- ics of emergent objectivity, and the analysis of non-objectivity in experimental and biology-inspired systems. Firstly, we propose two new mathematical frameworks to describe objec- tivity, Strong Quantum Darwinism and invariant spectrum broadcast structure. Then we unite them with the pre-existing frameworks by identifying their deep connections and differences. Each framework considers varying amounts of objec- tivity in the system and environments and together, they create a hierarchy of objectivity. We then analyse objectivity in a scenario where system-environment in- teractions are strong and non-Markovian, highlighting some practical differences between the Quantum Darwinism frameworks. Next, we describe the quantum channels that create objective states, leading us to discuss the contribution of non- Markovianity to the emergence of objectivity. Then, we introduce a witnessing scheme that simplifies the detection of non-objectivity to promote further exper- imental testing of Quantum Darwinism. Finally, we examine the contribution of quantum coherence and non-objectivity to the performance of a biological-inspired 6 quantum magnetic sensor. We find that the sensor operates in a non-objective regime, and that quantum coherence is necessary for the sensor's performance. While the quantum-to-classical transition remains unsolved, Quantum Dar- winism and its frameworks contribute to the understanding of emergent objectivity and have much potential to further explore aspects of the transition within the structure of quantum mechanics. Impact Statement The research presented in the thesis contributes to our understanding of the quantum-to-classical transition and the role of system-environment correlations in the transition. The unification of the frameworks of objectivity and Quantum Darwinism gives us a greater understanding on what it means for quantum systems to be objective through the lenses of quantum information, state structure and geometry, and furthermore provides nuance on what it means to be \objective". The new mathematical frameworks of Quantum Darwinism developed here can be immediately applied to study emergent objectivity in various system-environment scenarios. As a step towards experimental verification with current available tech- nological capabilities, the thesis includes research towards measuring objectivity in experimental systems. Our proposed scheme could be used to explore the quantum-to-classical transition through the lens of quantum Darwinism in larger and more realistic environment settings, which in turn will contribute to the understanding of the quantum-to-classical transition. In the thesis, we also contribute to the understanding of the operation of quantum biological systems. Quantum biological systems operate at the quantum- classical boundary: we have analysed the important role of the environment in maintaining the quantum nature of the biological systems while simultaneously enhancing function. This work can also contribute to quantum technological advancement by exploiting environment effects to enhance their operation, as near term quantum technologies will likely operate at a quantum-classical boundary similar to quantum biological systems. In the long term, this will impact in our understanding of the natural world regarding the quantum-to-classical transition 8 and the nature of physical reality at the smallest scales. The works in this thesis have also been disseminated through the pub- lication of papers for most of the following chapters, and numerous talks and poster presentations at conferences, workshops, and university visits in the UK and beyond. List of Publications and Preprints The work presented in this thesis contains results from the following papers/ preprints: [1] Thao P. Le and Alexandra Olaya-Castro, Objectivity (or lack thereof): • Comparison between predictions of quantum Darwinism and spectrum broad- cast structure, Phys. Rev. A 98, 032103 (2018). [2] Thao P. Le and Alexandra Olaya-Castro, Strong Quantum Darwinism • and Strong Independence are Equivalent to Spectrum Broadcast Structure, Phys. Rev. Lett. 122, 010403 (2019). [3] Thao P. Le, Quantum discord-breaking and discord-annihilating channels, • (2019), arxiv:1907.05440v1. [4] Thao P. Le and Alexandra Olaya-Castro, Witnessing non-objectivity in • the framework of strong quantum Darwinism, Quantum Sci. Technol. 5, 045012 (2020). Thao P. Le and Alexandra Olaya-Castro, A non-maximally mixed initial • state is necessary to detect magnetic field direction in an avian-inspired quantum magnetic sensor, (2020, in preparation) The following work was not including in this thesis: [5] Thao P. Le, Piotr Mironowicz, and Pawel Horodecki, Blurred quantum • Darwinism across quantum reference frames, (2020), arxiv:2006.06364v1. Acknowledgments Firstly, I would like to give a massive thank you to my supervisor, Alexandra Olaya-Castro, who is also my major co-author and collaborator. Our meetings and chats about physics and beyond, and her guidance and insight throughout have been invaluable to me. I am also very grateful for the freedom to follow and develop my own research ideas and interests. (And more pragmatically, the freedom to go on a fair number of conferences and visits and trips back home to Australia.) Next, I would like to thank all the people in my CDT Cohort, with whom we shared the pains and joys of the first masters year, and phd/life-related grievances there after: Diego Aparicio, Gioele Consani, Abdulah Fawaz, Matt Flinders, Ed Grant, Tom Hird, Gaz Jones, Tamara Kohler, Conor Mc Keever, Jamie Potter, James Seddon, Maria Stasinou, and James Watson. My CDT experience has been marked by Dan Browne's calm presence, with the appearances of Sougato Bose, Andrew Fisher, and Paul Warburton who no doubt do more behind the scenes than I know. And the person I would like to thank the most regarding the CDT is Lopa Murgai, who has been lovely and friendly and has been fundamental in making my years at the CDT smooth. There are many other people who have also made my experience at UCL and my phd years special. I would like to thank: the other members of Alexandra's group, Valentina Notararigo and Stefan Siwiak-Jaszek, which whom I shared sweet office discussions. Abbie Bray, with whom I shared heartwarming talks with. I had fun and am grateful for the opportunities to help with events at UCL led by Anson Mackay and Sergey Yurchenko. I would like to especially thank Carlo Sparaciari, Sofia Qvarfort, Lia Li, and Scott Melville who have all been so kindly 12 patient with my various and numerous questions about research and adjacent matters. Throughout my PhD, I enjoyed discussing research (more than once) with the following researchers (in no particular order): Marco Piani, Gerardo Adesso, Paul Knott, Philip Taranto, Pawe lHorodecki, Ryzard Horodecki, Piotr Mironow- icz, Thorsten Ritz, Clarice D. Aiello, Rodrigo G´omez, Siddhartha Das, and Graeme Pleasance. I had the great joy to visit National Quantum Information Centre (KCIK) and the University of Gda´nsk for a month in 2019, and for this, I especially thank Pawe lHorodecki for hosting my time in Sopot and Gdansk, as well as Piotr Mironowicz for the collaborative work we did. I would also like to thank the following people for having hosted me on visits: Pawe l Horodecki (see above), Clarice D. Aiello, Gerardo Adesso & Paul Knott, Berthold-Georg Englert, Simon Milz, and Kavan Modi. A lot of the work in this thesis could not have been completed without the help of the various anonymous referees who took the time to carefully read the work. Furthermore, this work and the four years would not be possible without the funding provided by the Engineering and Physical Sciences Research Council (Grant No. EP/L015242/1). I also thank my two examiners, Lluis Masanes and Gerardo Adesso, for their reading of this work and their comments and feedback. I thank my parents for their care and concern, and my siblings for their conversation at odds times in the day, games, and other such sibling things. I would also like to thank my online reading/writing friends (you know who you are!) for their cheerleading, and who all turned out to be equally academic|all the better to share the woes of academic/study life! And to re-iterate again, this thesis would not have been possible without Alexandra Olaya-Castro. Thank