Southwest Quantum Information and Technology

Bounds on relative entropy decay

Presenting Author: Nicholas LaRacuente, University of Illinois at Urbana-Champaign
Contributing Author(s): Li Gao, Marius Junge, Haojian Li

I will summarize our recent progress bounding the decay rates of relative entropy under different classes of quantum channels. These include modified logarithmic Sobolev inequalities for quantum Markov semigroups, their tensor-stable complete versions, state-independent comparisons of the relative entropy of channel outputs, and variations on subadditivity. The relative entropy underpins many resource measures and common entropy expressions, including coherence, asymmetry, and a variety of communication rates. Relative entropy generalizes naturally to infinite-dimensional settings, such as field theories in which the ordinary von Neumann entropy diverges. We use techniques from operator algebras and noncommutative geoemetry, as well as more familiar information-theoretic and variational approaches. Finally, I will discuss how the common form of relative entropy with respect to subalgebras or subspaces implies that particular classes of results automatically apply across a wide variety of resources and operational scenarios.

Read this article online: https://arxiv.org/abs/1909.01906, https://arxiv.org/abs/1807.08838

(Session : from 5:00pm - 7:00pm)