Quantum Brascamp-Lieb Dualities
Abstract
Brascamp-Lieb inequalities are entropy inequalities which have a dual formulation as generalized Young inequalities. In this work, we introduce a fully quantum version of this duality, relating quantum relative entropy inequalities to matrix exponential inequalities of Young type. We demonstrate this novel duality by means of examples from quantum information theory -- including entropic uncertainty relations, strong data-processing inequalities, super-additivity inequalities, and many more. As an application we find novel uncertainty relations for Gaussian quantum operations that can be interpreted as quantum duals of the well-known family of `geometric' Brascamp-Lieb inequalities.
Keywords
Cite
@article{arxiv.1909.02383,
title = {Quantum Brascamp-Lieb Dualities},
author = {Mario Berta and David Sutter and Michael Walter},
journal= {arXiv preprint arXiv:1909.02383},
year = {2023}
}
Comments
v3: 24 pages, minor changes, to appear in Commun. Math. Phys