Speaker: Iman Marvian (Duke University)
Title: From symmetric quantum circuits to quantum Fisher information metrics
Abstract: In this talk, I present an overview of two ongoing projects. First, I discuss quantum circuits with gates that respect a global symmetry or, equivalently, conserve a global charge, such as the total energy of the system. Recent studies have shown that, in the presence of symmetry, the locality of gates imposes severe restrictions on the set of realizable unitaries. I explain how the nature of these restrictions strongly depends on the properties of the symmetry. For instance, some restrictions arise exclusively in the case of non-Abelian symmetries. Additionally, I briefly discuss recent work on the statistical properties of random circuits with symmetry-respecting gates (arXiv:2408.14463).
In the second part of my talk, I present recent results on quantum Fisher information metrics and their applications in the resource theories of quantum thermodynamics and asymmetry. Specifically, I highlight a recent result that provides an operational interpretation of the RLD quantum Fisher information metric in the context of coherence distillation (arXiv:2409.05974).
About the seminar: Weekly seminar hosted by the Quantum Working Group. Topics include quantum information theory and related topics in operator algebra. Contact: Felix Leditzky (leditzky@illinois.edu)