Li Gao

Conditioning on Subalgebras - Entropy Duality and Generalized Quantum Stein's Lemma in von Neumann Algebras

We establish duality relations for conditional entropies relative to subalgebras of arbitrary von Neumann algebras, including the Umegaki relative entropy as well as the sandwiched- and Petz-R\'enyi divergences. Even in finite dimensions, these results extend the familiar dualities for conditional entropies from tensor...