Christa Zoufal, David Sutter, et al.
Physical Review Applied
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.
Christa Zoufal, David Sutter, et al.
Physical Review Applied
Tony Metger, Omar Fawzi, et al.
FOCS 2022
Christophe Piveteau, David Sutter, et al.
Physical Review Letters
Christophe Piveteau, David Sutter, et al.
npj Quantum Information