Affiliation:
1. University of Chicago, Chicago, Illinois 60637, USA
Abstract
Purely multiplicative comparisons of quantum relative entropy are desirable but challenging to prove. We show such comparisons for relative entropies between comparable densities, including the relative entropy of a density with respect to its subalgebraic restriction. These inequalities are asymptotically tight in approaching known, tight inequalities as perturbation size approaches zero. Based on these results, we obtain a kind of inequality known as quasi-factorization or approximate tensorization of relative entropy. Quasi-factorization lower bounds the sum of a density’s relative entropies to several subalgebraic restrictions in terms of its relative entropy to their intersection’s subalgebraic restriction. As applications, quasi-factorization implies uncertainty-like relations, and with an iteration trick, it yields decay estimates of optimal asymptotic order on mixing processes described by finite, connected, undirected graphs.
Funder
IBM
University of Illinois at Urbana-Champaign, Department of Physics
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Cited by
2 articles.
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