Quantum Foundations

A standard approach to quantifying resources is to determine which operations on the resources are freely available and to deduce the ordering relation among the resources that these operations induce. If the resource of interest is the nonclassicality of the correlations embodied in a quantum state, that is, entanglement, then it is typically presumed that the appropriate choice of free operations is local operations and classical communication (LOCC). We here argue that, in spite of the near-universal endorsement of the LOCC paradigm by the quantum information community, this is the wrong choice for one of the most prominent applications of entanglement theory, namely, the study of Bell scenarios. The nonclassicality of correlations in such scenarios, we argue, should be quantified instead by local operations and shared randomness (LOSR). We support this thesis by showing that various perverse features of the interplay between entanglement and nonlocality are merely an artifact of the use of LOCC-entanglement and that the interplay between LOSR-entanglement and nonlocality is natural and intuitive. Specifically, we show that the LOSR paradigm (i) provides a resolution of the "anomaly of nonlocality", wherein partially entangled states exhibit more nonlocality than maximally entangled states, (ii) entails a notion of genuine multipartite entanglement that is distinct from the conventional one and which is free of several of its pathological features, and (iii) makes possible a resource-theoretic account of the self-testing of entangled states which simplifies and generalizes prior results. Along the way, we derive some fundamental results concerning the necessary and sufficient conditions for convertibility between pure entangled states under LOSR and highlight some of their consequences, such as the impossibility of catalysis for bipartite pure states. 

Defining a generic quantum system requires, together with a Hilbert space and a Hamiltonian, the introduction of an algebra of observables, or equivalently a tensor product structure. Assuming a background time variable, Cotler, Penington and Ranard showed that the Hamiltonian selects an almost-unique tensor product structure. This result has been advocated by Carrol and collaborators as supporting the Everettian interpretation of quantum mechanics and providing a pivotal tool for quantum gravity. In this talk I argue against this, on the basis of the fact that the Cotler-Penington-Ranard result does not hold in the generic background-independent case where the Hamiltonian is replaced by a Hamiltonian constrain. This reinforces the understanding that entropy and entanglement, that in the quantum theory depend on the tensor product structure, are quantities that are observable dependent. To conclude, I would like to pose the question of whether clocks can be thought as a resource, and how thinking of time in terms of physical clocks can inform our interpretation of quantum mechanics

Causal reasoning is vital for effective reasoning in science and medicine. 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. However, all previous approaches to machine-learning assisted diagnosis, including deep learning and model-based Bayesian approaches, learn by association and do not distinguish correlation from causation. I will show that these approaches systematically lead to incorrect diagnoses. I will outline a new diagnostic algorithm, based on counterfactual inference, which captures the causal aspect of diagnosis overlooked by previous approaches and overcomes these issues. I will additionally describe recent algorithms from my group which can discover causal relations from uncontrolled observational data and show how these can be applied to facilitate effective reasoning in medical settings such as deciding how to treat certain diseases.