Complexity Forum

Speaker: Tobias Galla (University of Manchester)

Title: Complexity measures, information projections and quantum exponential families

Abstract: I will discuss a set of existing complexity measures for classical multi-particle systems, based on exponential families and related concepts of information geometry. We show that these measures can increase under local transformations and when individual degrees of freedom are integrated out. For example a local transformation acting on a single particle in an N-particle system may turn 2-particle correlations into 3-particle correlations. This limits the interpretation of such measures as a quantifier for complexity or correlations. We propose a refined definition, investigate its properties and discuss its numerical evaluation. As an example, we study coupled logistic maps.
In the second part of the talk I will discuss similar complexity measures for N-qubit quantum states. Specifically, we use the distance from the exponential family of thermal states of k-particle Hamiltonians as a measure of complexity (k<N). I will show how symmetries can be exploited to simplify the resulting optimisation problem, and I will present a numerical algorithm for the computation of this complexity measure.