Speaker
Description
Mutual information (MI) and conditional mutual information (CMI) are central tools to characterize the correlation and entanglement in quantum systems. However, their universal properties in quantum many-body systems were poorly understood before. In this talk, I will present our recent rigorous results on the universal properties of MI and CMI in gapped quantum matter, and discuss their interesting applications. Our central theorems state that, for local spin and fermionic systems in any spatial dimension, the super-polynomial decay behavior of MI and CMI is a universal property of gapped quantum phases, i.e., all systems in such a phase possess this property if one system in this phase possesses this property. Moreover, I will explain that the MI and CMI indeed decay superpolynomially in most (if not all) known topological phases, which leads to interesting implications on how to dynamically prepare anyons and how symmetries act on topological phases.