Compositional Foundations of Physics Team

Team Leader: John Harry Selby

“Answering fundamental questions through a compositional lens.”

The team's objective is to tackle fundamental questions in quantum theory from applied questions such as “how do we optimise resources for a quantum computer?” to foundational questions such as “how should we understand causality in the quantum world?”. The way we approach these questions is from a compositional perspective, in particular, using tools and ideas developed in the field of applied category theory.

Activity

The team’s research agenda focuses on the following topics:

Causality – Bell’s theorem can be posed as a challenge to the standard frameworks (e.g., Pearls DAG formalism) for studying causation. We seek to develop alternative frameworks which, on the one hand, subsume the standard ones, and, on the other hand, are still applicable within the quantum world. In the long run, we believe that understanding quantum causation will hold the key to understanding the ontology of quantum theory.

Nonclassicality – It is now commonly accepted that there is no going back to our pre-quantum, classical, world-view. Nevertheless, exactly how to best understand the nonclassicality of quantum theory, how to quantify it, and how to use it as a resource, remain important open problems. We tackle such problems, in particular, via one of the leading notions of classicality known as generalised noncontextuality which is based on Leibniz’s principle of the identity of indiscernibles.

Computation – Quantum computers are promised to revolutionise many areas of science and technology. Yet, in order for any of these promises to have any chance of becoming reality, we will need to understand how to make best use of the quantum resources available to us. However, several fundamental problems serve as roadblocks to this goal. For example, wide gulf between resources typically studied by quantum theorists (such as coherence, nonlocality, …) and those which are relevant to real world hardware (such as T-gate count, circuit depth,…). We aim to incorporate these “real world’’ issues into more abstract resource theory frameworks in order to develop optimisation techniques which can take these into account.

Symmetries – Much of modern theoretical physics is built on the study of symmetries, yet many of our foundational tools, such as generalised probabilistic theories and ontological models, do not take these into consideration. We aim to resolve this by extending these tools to take into account symmetries and to investigate what this means, e.g., for the nonclassicality of nature. That is, we extend our best operational frameworks to account for unspeakable as well as speakable information.

Spacetime – Quantum information processing typically viewed, at least implicitly, as taking place within some background spacetime. For example, exploiting our understanding of our fundamental spacetime in order to carry out a loophole free Bell test, or overcoming the limitations of effective spacetimes imposed by limited qubit connectivity in some given quantum computer. Despite its fundamental importance, spacetime is typically neglected from the theoretical description of the quantum protocol. We are developing new tools to directly incorporate the spacetime structure and so, to be able to more systematically take it into account when, for example, developing new information processing protocols.

Keywords: compositionality, process theories, generalised contextuality, ontological models, causation, symmetry, spacetime, categorical quantum mechanics, generalised probabilistic theories, computational resources, nonclassicality, graphical calculi.