This series consists of talks in the area of Foundations of Quantum Theory. Seminar and group meetings will alternate.
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.
Weak values are quantities accessed through quantum experiments involving weak measurements and post-selection. It has been shown that ‘anomalous’ weak values (those lying beyond the eigenvalue range of the corresponding operator) defy classical explanation in the sense of requiring contextuality [M. F. Pusey, Phys. Rev. Lett. 113, 200401, arXiv:1409.1535]. We elaborate on and extend that result in several directions. Firstly, the original theorem requires certain perfect correlations that can never be realised in any actual experiment.
In the framework of ontological models, the features of quantum
theory that emerge as inherently nonclassical always involve properties that
are fine tuned, i.e. properties that hold at the operational level but break at the
ontological level (they only hold for fine tuned values of the ontic parameters). Famous
Schur-Weyl duality, arising from tensor-power representations of the unitary group, is a big useful hammer in the quantum information toolbox. This is especially the case for problems which have a full unitary invariance, say, estimating the spectrum of a quantum state from a few copies. Many problems in quantum computing have a smaller symmetry group: the Clifford group. This talk will show how to decompose tensor-power Clifford representations through a Schur-Weyl type construction. Our results are also relevant for the theory of Howe duality between symplectic and orthogonal groups.
Bell inequalities are important tools in contrasting classical and quantum behaviors. To date, most Bell inequalities are linear combinations of statistical correlations between remote parties. Nevertheless, finding the classical and quantum mechanical (Tsirelson) bounds for a given Bell inequality in a general scenario is a difficult task which rarely leads to closed-form solutions. Here we introduce a new class of Bell inequalities based on products of correlators that alleviate these issues. Each such Bell inequality is associated with a non-cooperative coordination game.
The no-signalling principle, preventing superluminal communication and the consequent logical paradoxes, is typically formulated within the information-theoretic framework in terms of admissible correlations in composite systems. In my talk, I will present its complementary incarnation associated with dynamics of single systems subject to invasive measurements. The `dynamical no-signalling principle' applies to any theory with well defined rules of calculating detection statistics in spacetime.