Noncommutative Geometry Seminar
Date: March 29, 2024
Time: 2:00PM - 3:00PM
Location: BLOC 306
Speaker: Zishuo Zhao, Tsinghua University
Title: Relative entropy between bimodule quantum channels
Abstract: We propose a notion of relative entropy between bimodule quantum channels on finite von Neumann algebras, generalizing the remarkable Pimsner-Popa entropy for subfactors. We will discuss various inequalities of this relative entropy. In particular, the relative entropy of bimodule quantum channels is bounded by the relative entropy of their Fourier multipliers, which is a higher analogue of relative entropy of states. The equality holds if the inclusion of von Neumann algebras admits a downward Jones basic construction.