My research is focused on the foundations of physics seeking to answer questions such as: "how do we know that Nature is non-classical?", "is there any deeper theory of Nature than quantum theory?", and "what is the best way to understand quantum theory?".
The key tools that I employ include process theories, categorical quantum mechanics, resource theories, and generalised probabilistic theories. In particular, using novel diagrammatic techniques which offer intuitive methods for tackling complex problems.
Process theories are a novel tool for studying nature built on the mathematics of symmetric monoidal category theory. One key benefit to this approach is that it provides a diagrammatic calculus that makes reasoning intuitive. Process theories have formed the foundation of the majority of my work, for instance leading to a novel reconstruction of quantum theory from diagrammatic principles, arXiv:1802.00367 talk available on PIRSA. The second key benefit is that the so-called "landscape" of physical theories described my process theories is much richer than that of alternative approaches, for instance, allowing us to study emergent behaviour and the relationship between different physical theories.
Nonclassicality of Nature
How do we know that Nature is not classical? What is the fundamental point of divergence between quantum and classical theory? This is precisely the sort of question that one can formally ask within the process theory framework. In particular I have, with colleges at PI, studied Spekkens' notion of Generalised Noncontextuality from this perspective leading to a new framework for describing ontological models and operational theories and hence anew understanding of nonclassicality of Nature. See the talk on PIRSA by my collaborator David Schmid and arXiv:1911.10386.
Why does the world appear to us to be classical? What is it about quantum theory which keeps it so well hidden? Again the process theory framework is ideally suited to tackling such questions providing us with a general notion of what it means for one theory to decohere to another, see arXiv:1701.07404 and arXiv:1701.07400, see also the talk at QPL 2017 by Sean Tull. We can then investigate what properties a theory must have in order to permit emergent classicality via decoherence, in particular, in arXiv:1705.08028, we show that entanglement is a necessary feature of a theory to decohere to classical theory.
Theories beyond quantum
Is quantum theory the ultimate theory of Nature, or is there some deeper theory of Nature yet to be discovered? Building on our work on emergent classicality we can start to investigate emergent quantality -- that is, if there is indeed some deeper theory of Nature, then there must be some explanation within that theory for why we have not seen it in current experiments. In arXiv:1701.07449 we propose one such mechanism called hyperdecoherence and show which intuitive features of quantum theory we may have to give up on to go beyond quantum theory. See the talk by Ciarán M. Lee from QPL 2017.
To understand what we can do within any particular physical theory we need to know what resources that theory possesses. This is what the study of resource theories enables. In particular, a unifying framework due to Coecke, Fritz and Spekkens allows for the study of the inter-conversion and composition of resources, is based on the notion of a process theory. This allows for us to study resources beyond those which are typically considered in the literature, for example, viewing channels, measurements and higher-order transformations as examples of resources to be studied. In my research I applied these methods to the study of the resource theory of coherence arXiv:1911.04514 which highlighted the deficiencies in the existing definitions and revealed connections between previously disparate seeming notions of coherence.
Computation and cryptography in GPTs
To understand how quantum theory enables technological advantages it is useful to view quantum theory from the outside, that is, as one particular theory within a landscape of physical theories. That way we can modify different aspects of the theory to see how the information processing capabilities change. The framework of generalised probabilistic theories is ideally suited to this study as it provides the necessary structure to be able to be easily compared with quantum theory. In particular, during my PhD collaborators and I have studied the structure of quantum computation arXiv:1604.03118, arXiv:1510.04699 and arXiv:1704.05043 within this framework. More recently, Jamie Sikora and I combined tools from convex optimisation theory, in particular conic programs and semi-infinite programs, with the GPT framework to study quantum cryptography, see arXiv:1901.04876 arXiv:1803.10279 and arXiv:1711.02662.