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.

arXiv commentv3: 24 pages, minor changes, to appear in Commun. Math. Phys

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Cited by in corpus (5)

• Complete entropic inequalities for quantum Markov chains
• On contraction coefficients, partial orders and approximation of capacities for quantum channels
• Continuity of quantum entropic quantities via almost convexity
• A game of quantum advantage: linking verification and simulation
• The generalized strong subadditivity of the von Neumann entropy for bosonic quantum systems