Quantum causal modelling

Background, Context and Impact
Classical causal models give explanations of statistical correlations by providing a causal structure that could give rise to them. They have helped us to answer fundamental questions concerning the nature of causal influence, and the constraints that patterns of causal influence place on data. They have widespread practical application, since if one understands the causal situation underlying statistical correlations, one is more likely to accurately predict the result of changing some of the statistical parameters in future interventions. This applies to machines just as much as to humans, hence classical causal models are a key topic in the fields of AI and machine learning.
However, it has long been known that paradigmatic features of quantum theory (such as `quantum nonlocality') cannot be given a causal explanation by classical standards. Hence recent years have seen the development of a variety of approaches to causal modelling in the presence of quantum systems and devices. The project will develop new forms of causal modelling designed specifically for quantum systems. This is of importance for fundamental science, enabling us to answer basic questions concerning the nature of causal influence in a quantum universe, such as whether causal relationships are relative to an agent or a reference frame, and whether causal relationships are directed in time. It is also practically important. Once quantum devices, or networks of devices, become larger than the current small-scale prototypes, full tomography of the device becomes impossible. This means that verification of the correct functioning of a device or network must be based only on limited data. Quantum causal modelling promises a distinctly causal approach to the problem of verification, wherein inferences about the causal structure of the device or network are made from limited data, and then used to predict future behaviour under different parameters.
This project falls within the EPSRC Physical Sciences and Quantum Technologies research areas.
Aims
The project is theoretical in nature, not involving experiment or large-scale computation. The aims of the project include:
(1) Develop new methods for causal discovery, able to discriminate correlations produced by classical devices from those that require particular arrangements of quantum devices.
(2) Characterize the causal structure of reversible (i.e., unitary) transformations in quantum theory.
(3) (More ambitious.) Develop a model of emergent space-time from a network of fundamental quantum causal relationships.

Novel research methods
The research methodology is interdisciplinary: the project will combine insights and results from the existing literature on classical causal modelling with the formalism of quantum information theory. Specific methodologies applied to the aims above include:
(1) Develop information theoretic quantities that generalise the standard notions of entropy and mutual information to quantum systems that are causally related to one another (e.g., are separated in time).
(0) Develop and make use of new forms of diagrammatic notation. This will extend existing work that uses category theory to describe quantum processes, to a framework that is explicitly tailored for representing quantum causal structure.
(2) Approach the problem in a similar manner to existing works, which model emergent spatial relations from a network of quantum systems, but extend the approach to include both space and time as a single entity.