Nonclassicality, as witnessed by the incapacity of Classical Causal Theory (CCT) of explaining a system's behavior given its causal structure, come to be one of the hottest topics in Quantum Foundations over the last decades, a movement that was motivated both by its vast range of practical applications and by the powerful insights it provides about the rules of the quantum world. Among the many attempts at understanding/quantifying this phenomenon, we highlight the idea of inquiring how further would it be necessary to relax the causal structure associated with a given system in order to have its nonclassical behavior explained by CCT. More recently, we showed that the relaxation demanded to explain the behavior of a subset of variables in a given experiment may not be allowed by the embedding causal structure when considering the behavior of the remaining variables, which led to a new way of witnessing nonclassicality. In this seminar, we discuss a new way of quantifying this incompatibility and possible generalizations of this approach to different scenarios.
This lecture is devoted to Noether’s theorems and the study of the interplay between symmetries and conservation laws, from ordinary mechanics to general relativity. In order to start on a common ground and interest a broad audience, we will begin with a review of Noether’s (first) theorem in ordinary non-relativistic mechanics. This will enable us to settle some subtleties, agree on conventions, and especially explore some curious and lesser-known symmetry features of familiar models (such as particles and celestial mechanics). We will then move on to field theory, and discuss the construction of conserved currents and energy-momentum tensors. This will include a discussion of conserved quantities in general relativity. Finally, we will turn to the core of the topic, which is Noether’s (second) theorem for gauge symmetries. After recalling the basic properties of gauge theories in Lagrangian and Hamiltonian form, we will derive the consequences of gauge symmetry for the construction of conserved charges. For this, we will introduce the so-called covariant phase space formalism, which enables to construct symmetry charges and algebras, and derive (non) conservation laws. This will be illustrated in Maxwell’s theory and in general relativity. In particular, we will focus in depth on the example of three-dimensional gravity as an exactly soluble model in which all aspects of symmetries can be understood. We will end with an outlook towards the notion of asymptotic symmetries and their use in classical and quantum gravity.
Ideally, the audience should be familiar with:
basic features of general relativity
In this talk, I present the latest works on anyonic information theory and how it is linked to aspects of quantum foundations. First, the theory of 2+1 D non-abelian anyons will be introduced. The newly discovered notion of anyonic creation operators will be presented, as well as their use as local elements of reality within the Deutsch-Hayden interpretation of quantum mechanics. Lastly, I will show strange properties of anyonic entanglement that appear due to the lack of a tensor product structure, such as the different spectra of marginals in bipartite systems. This property makes the Von Neumann entropy a bad entanglement measure. I will explain the challenges of defining entanglement measures for anyonic systems and current approaches.