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Causal reasoning is vital for effective reasoning in many domains, from healthcare to economics. In medical diagnosis, for example, a doctor aims to explain a patient’s symptoms by determining the diseases causing them. This is because causal relations, unlike correlations, allow one to reason about the consequences of possible treatments and to answer counterfactual queries. In this talk I will present some recent work done with my collaborators about how one can learn and reason with counterfactual distributions, and why this is importantly for decision making. In all cases I will strive to motivate and contextualise the results with real word examples.

It is not explicitly obvious that relativity and quantum mechanics are consistent with each other. Extensive research has shown that quantum states are consistent with relativity, in that they do not allow for faster-than-light transferring of information. In contrast, much less research has been done in quantum measurements, and in fact, naive attempts to put together relativity and quantum measurements lead to signaling between space-like separated regions. In this talk I will describe how this same problem arises in non-relativistic quantum physics, where measurements on systems kept spatially separated in general lead to signalling. By giving away the projection postulate, it is possible to alleviate this problem and measure non-local variables without signaling by exploiting pre-shared entanglement as a resource. I will describe a protocol for implementing any joint measurement in a non-signaling manner, and argue that this leads to a complete classification of all joint quantum measurements, based on the required amount of entanglement necessary to measure them.

We propose that Bell correlations are explicable as a combination of (i) collider bias and (ii) a boundary constraint on the collider variable. We show that the proposal is valid for a special class of ('W-shaped') Bell experiments involving delayed-choice entanglement swapping, and argue that it can be extended to the ordinary ('V-shaped') case. The proposal requires no direct causal influence outside lightcones, and may hence offer a way to reconcile Bell nonlocality and relativity.

Given the large number of proposed quantum machine learning (QML) algorithms, it is somewhat surprising that ideas from this field have not yet been extended to causal learning. While deep learning and generative machine learning models have taken centre stage in the industrial application of automated learning on classical data, it is nonetheless well known that these techniques don't reliably capture causal concepts, leading to significant performance vulnerabilities. Increasingly, classical ML experts are taking ideas from causal inference, a field traditionally limited to small data sets of low dimensionality, and injecting modern ML elements to create new algorithms that benefit from the best of both worlds. These hybrid classical approaches provide new opportunity to search for potential quantum advantage. In this talk I explore this new research direction and propose several new quantum algorithms for classical causal inference.

Non-Hermitian Hamiltonians are a compulsory aspect of the linear dynamical systems that model many physical phenomena, such as those in electrical circuits, open quantum systems, and optics. Additionally, a representation of the quantum theory of closed systems with non-Hermitian observables possessing unbroken PT-symmetry is well-defined.   In this talk, I will second-quantize non-Hermitian quantum theories with paraFermionic statistics. To do this, I will introduce an efficient method to find conserved quantities when the Hamiltonian is free or translationally invariant. Using a specific non-Hermitian perturbation of the Su-Schrieffer-Heeger (SSH ) model, a prototypical topological insulator, I examine how PT-symmetry breaking occurs at the topological phase transition. Finally, I show that although finite-dimensional PT-symmetric quantum theories generalize the tensor product model of locality, they never permit Bell inequality violations beyond what is possible in the Hermitian quantum tensor product model.