Mathematical Physics

A very general way of describing the abstract structure of quantum theory is to say that the set of observables on a quantum system form a C*-algebra.  A natural question is then, why should this be the case - why can observables be added and multiplied together to form any algebra, let alone of the special C* variety?  I will present recent work with Markus Mueller and Howard Barnum, showing that the closest algebraic cousins to standard quantum theory, namely the Jordan-algebras, can be characterized by three principles having an informational flavour, namely: (1) a generalized spectral decomposition, (2) a high degree of symmetry, and (3) a requirement on conditioning on the results of observations.   I'll then discuss alternatives to the third principle, as well as the possibility of dropping it as a way of searching for natural post-quantum theories.

This talk will be about non-equilibrium many-body physics in integer quantum Hall edge states far from equilibrium. Recent experiments have generated a highly non-thermal electron distribution by bringing together at a point contact two quantum Hall edge states originating from sources at different potentials. The relaxation of this distribution to a stationary form is observed as a function of distance downstream from the contact [Phys. Rev. Lett. 105, 056803 (2010)]. I will discuss the broader context for the experiments and a physical picture of the equilibration process. I will also present an exact treatment of a minimal model for the experiment with results that account well for the observations. [Joint work with Dmitry Kovrizhin]

We discuss the extension of the smooth entropy formalism to arbitrary physical systems with no bound on the number of degrees of freedom, comparing them with already existing notions of entropy for infinite-dimensional systems. Our analysis is both conceptual as well as based on operational primitives, for example we ask for the ability to perform privacy amplification against any kind of quantum side information.  As an application, we show how to employ a version of the entropic uncertainty relation to provide a security analysis for continuous variable quantum key distribution protocols.   based on arXiv:1107.5460, 1112.2179. This is joint work with Mario Berta, Fabian Furrer as well as with Torsten Franz, Marco Tomamichel, Reinhard Werner