Quantum Physics

Quantum theory is the most accurate scientific theory humanity has ever devised. But it is also the most mysterious. No one knows what the underlying picture of reality at quantum level is. This presentation will introduce you to some of the many interpretations of quantum theory that scientists have devised and discuss the infamous 'measurement problem'.

Violation of local realism can be probed by theory–independent tests, such as Bell’s inequality experiments. There, a common assumption is the existence of perfect, classical, reference frames, which allow for the specification of measurement settings with arbitrary precision. However, if the reference frames are ``bounded'', only limited precision can be attained. We expect then that the finiteness of the reference frames limits the observability of genuine quantum features. Using spin coherent states as reference frames, we determined their minimal size necessary to violate Bell’s inequalities in entangled systems ranging from qubits to macroscopic dimensions. In the latter, the reference frame’s size must be quadratically larger than that of the system. Lacking such large reference frames, precludes quantum phenomena from appearing in everyday experience.

Although most realistic approaches to quantum theory are based on classical particles, QFT reveals that classical fields are a much closer analog. And unlike quantum fields, classical fields can be extrapolated to curved spacetime without conceptual difficulty. These facts make it tempting to reconsider whether quantum theory might be reformulated on an underlying classical field structure. This seminar aims to demonstrate that by changing only how boundary conditions (BCs) are imposed on ordinary classical field equations, a psi-epistemic quantum theory naturally emerges. Uncertainty and basic quantization naturally result from imposing BCs on closed hypersurfaces (as in Lagrangian QFT); further quantization results from extending Hamilton's principle to restrict the BCs as well as the field equations. The partial dependence of field parameters on future BCs implies an effective contextuality, naturally avoiding the usual arguments against realistic quantum models. Successful applications to the relativistic scalar field will be presented, further motivating an ambitious research program of reformulating quantum theory in terms of ontic classical fields.

We give a mathematical framework to describe the evolution of quantum systems subject to finitely many interactions with classical apparatuus and with each other. The systems in question may be composed of distinct, spatially separated subsystems which evolve independently, but may also interact. The evolution is coded in a mathematical structure in such a way that the properties of causality, covariance and entanglement are faithfully represented. The key to this scheme is to use a special family of spacelike slices -- we call them locative -- that are not so large as to permit acausal influences but large enough to capture nonlocal correlations. I will briefly describe how the dynamics can be described as a functor to a suitable category of Hilbert spaces and will also give some connections with logic.

We sketch some ideas about how higher-dimensional categories could be used to extend conventional quantum mechanics. The physical motivation comes from quantum field theory, for which higher-dimensional category theory is very relevant. We discuss how this new approach would affect familiar aspects of quantum theory, such as observables and the Copenhagen interpretation. Few solid answers will be given, but hopefully some discussion will be generated!

Tensor product is described in a family of categories that includes Set and Hilbert spaces. Such categories admit a "scalar" object which enables a definition of bi-arrows with two domains, generalizing functions of two variables. The tensor product is characterized by the expected universal property relating bi-arrows to arrows.

This talk will present an overview of work done in the past decade on quantum state and process tomography, describing the basic notions at an introductory level, and arguing for a pragmatic approach for data reconstruction. The latest results include recent numerical comparison of different reconstruction techniques, aimed at answering the question: "is 'the best' the enemy of 'good enough'?"