We develop reverse versions of hypercontractive inequalities for quantum channels. By generalizing classical techniques, we prove a reverse hypercontractive inequality for tensor products of qubit depolarizing channels. We apply this to obtain a rapid mixing result for depolarizing noise applied to large subspaces, and to prove bounds on a quantum generalization of non-interactive correlation distillation.
@article{arxiv.1504.06143,
title = {Quantum reverse hypercontractivity},
author = {Toby Cubitt and Michael Kastoryano and Ashley Montanaro and Kristan Temme},
journal= {arXiv preprint arXiv:1504.06143},
year = {2016}
}
Comments
14 pages; v2: minor corrections and clarifications, essentially published version