Talks

Recently, a web of quantum field theory dualities was proposed linking several problems in the study of strongly correlated quantum critical points and phases in two spatial dimensions. These dualities follow from a relativistic flux attachment duality, which relates a Wilson-Fisher boson with a unit of attached flux to a free Dirac fermion. While several derivations of members of the web of dualities have been presented thus far, none explicitly involve the physics of flux attachment, which in relativistic systems affects both statistics and spin. We discuss how this can be achieved in models of relativistic current loops, where the concept of relativistic flux attachment can be made precise. In this context, we provide simple, explicit “derivations” of members of the web of dualities. We describe some implications of this work for relativistic composite fermion theories arising in condensed matter physics, as well as new possibilities for deriving additional dualities using these techniques.

For many optimal measurement problems of interest, the problem may be re-cast as a semi-definite program, for which efficient numerical techniques are available. Nevertheless, numerical solutions give limited insight into more general instances of the problem, and further, analytical solutions may be desirable when an optimised measurement appears as a sub-problem in a larger problem of interest. I will discuss analytical techniques for finding optimal measurements for state discrimination with minimum error and present applications to studying the gap between the theoretically optimal measurement and simpler, experimentally achievable schemes for bi-partite measurement problems.