This series consists of talks in the area of Foundations of Quantum Theory. Seminar and group meetings will alternate.
A proposal is made for a fundamental theory, in which the history of the universe is constituted of views of itself. Views are attributes of events, and the theory's only be-ables; they comprise information about energy and momentum transferred to an event from its causal past.
Using a process-theoretic formalism, we introduce the notion of a causal-inferential theory: a triple consisting of a theory of causal influences, a theory of inferences (of both the Boolean and Bayesian varieties), and a specification of how these interact. Recasting the notions of operational and realist theories in this mold clarifies what a realist account of an experiment offers beyond an operational account.
The compatibility-hypergraph approach to contextuality (CA) and the contextuality-by-default approach (CbD) are usually presented as products of entirely different views on how physical measurements and measurement contexts should be understood: the latter is based on the idea that a physical measurement has to be seen by a collection of random variables, one for each context containing that measurement, while the imposition of the non-disturbance condition as a physical requirement in the former precludes such interpretation of measurements.
To analyze the performance of adaptive measurement protocols for the detection and quanti cation of state resources, we introduce the framework of quantum preparation games. A preparation game is a task whereby a player sequentially sends a number of quantum states to a referee, who probes each of them and announces the measurement result. The measurement setting at each round, as well as the final score of the game, are decided by the referee based on the past history of settings and measurement outcomes.
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).
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.
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.
A superoscillatory function is a bandlimited function that, on some interval, oscillates faster than the highest frequency component shown in the function's Fourier transform. Superoscillations can be arbitrarily fast and of arbitrarily long duration but come at the expense of requiring a correspondingly large dynamic range. I will review how superoscillatory wave forms can be constructed and I will discuss the unusual behavior of wave functions that superoscillate. For example, they can describe particles that automatically strongly accelerate when passing through a slit.
We consider a consistent theory of classical systems coupled to quantum ones. The dynamics is linear in the density matrix, completely positive and trace-preserving. We apply this to construct a theory of classical gravity coupled to quantum field theory. The theory doesn't suffer the pathologies of semi-classical gravity and reduces to Einstein's equations in the appropriate limit.
Can a relativistic quantum field theory be consistently described as a theory of localizable particles? There are many well-known obstructions to such a description. Here, we trace exactly how such obstructions arise in the regime between nonrelativistic quantum mechanics and relativistic quantum field theory. Perhaps unexpectedly, we find that in the nonrelativistic limit of QFT, there are persisting issues with the localizability of particle states.