Southwest Quantum Information and Technology

Multiplicative Quantum Relative Entropy Comparison and Quasi-factorization

Presenting Author: Nicholas LaRacuente, University of Chicago

Purely multiplicative comparisons of quantum relative entropy are desirable but challenging to prove. We show such comparisons for relative entropies between comparable densities, including subalgebra-relative entropy and its perturbations. These inequalities are asymptotically tight in approaching known, tight inequalities as perturbation size approaches zero. Following, we obtain a quasi-factorization inequality, which compares the relative entropies to each of several subalgebraic restrictions with that to their intersection. We apply quasi-factorization to uncertainty-like relations and to conditional expectations arising from graphs. Quasi-factorization yields decay estimates of optimal asymptotic order on mixing processes described by finite, connected, undirected graphs.

Read this article online: https://arxiv.org/abs/1912.00983

(Session 5 : Thursday from 12:00pm-2:00 pm)