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.