A dialogue between quantum information and thermodynamics

Thermodynamics has always been inextricably linked with the abstract concept of information. The past decades have proved this relationship fruitful once again with the incorporation of many concepts and ideas from quantum information theory into the context of thermodynamics. This has allowed us to better understand the role played by uniquely quantum features such as coherence and entanglement in thermodynamics and encouraged us to test some of the fundamental limitations of thermodynamics within quantum physics laboratories. In this thesis I will demonstrate some of these fruits that allow us to both reformulate and test thermodynamics while forcing us to operationally understand the thermodynamic implications of our abstract information based results. Chapter 1 begins by following the historical and conceptual bridge linking thermodynamics and information, in particular how our usage of entropy in defining our underlying particle ensembles naturally imbues our theory of thermodynamics with information theoretic overtones. I will also introduce many of the tools and concepts that will be employed in the following chapters, including resource theoretic formulations, quantum particles and fluctuation relations. In chapter 2 we study the process of assisted work distillation. This scenario arises when two parties share a bipartite quantum state and their task is to locally distill the optimal amount of work when one party is restricted to thermal operations, whereas the other can perform general quantum operations and they are allowed to communicate classically. We find that this question is intimately related to the distillation of classical and quantum correlations. In chapter 3 we investigate manipulations of pure quantum states under incoherent or strictly incoherent operations assisted by a coherence battery, that is, a storage device whose degree of coherence is allowed to fluctuate in the process. This leads to the derivation of fluctuation relations for quantum coherence, analogous to Jarzynski's and Crooks' relations for work in thermodynamics. In chapter 4 we study a quantum analogue of the famous classical Gibbs paradox. This paradox forces us to take a closer look at our notion of distinguishability and the role of the observer in classical thermodynamics. Namely will an observer calculate an entropy change when two different classical gasses mix if, for said observer, the gasses cannot be distinguished. By moving the thought experiment into the quantum realm, we reveal new and surprising behaviour. We show that the ignorant observer, who cannot distinguish the gases with devices in their lab, can in fact extract work from mixing. This effect demonstrates the importance of carefully accounting for the level of knowledge of an observer, and its implications for genuinely quantum modifications to thermodynamics. In the final chapter 5 we look further at the properties of these identical quantum particles. In particular, because of their exchange symmetry, identical particles can appear to be entangled--where a complete description of a physical system cannot be gained from an understanding of its parts. However, a long-standing debate has questioned whether identical particle entanglement is physical or merely a mathematical artefact. In this chapter we provide such particle entanglement with a consistent theoretical description which we believe provides the resolutive step in this enduring debate and solidify our claim by using our tools to provide the first experimental quantitative estimation of identical particle entanglement. It is hoped that the content of these chapters will both inform and convince the reader that the role of quantum information in thermodynamics is complex and fruitful. That when we look deeper at the implicit presence of information in our theory of thermodynamics we can better understand how such a theory may be consistently merged with quantum theory. In addition, it is hoped that with the specific focus on the state space behaviour of quantum particles and the chapter studying the incongruous behaviour of a quantum Gibb's paradox that this thesis may motivate further studies into the emerging field of many-body quantum thermodynamics