Quantum reverse hypercontractivity

TL;DR

This paper introduces reverse hypercontractive inequalities for quantum channels, specifically tensor products of qubit depolarizing channels, leading to new results in rapid mixing and quantum correlation distillation.

Contribution

It generalizes classical reverse hypercontractivity to quantum channels and applies it to quantum information tasks like mixing and correlation distillation.

Findings

Proves reverse hypercontractive inequality for quantum channels

Establishes rapid mixing results for depolarizing noise

Provides bounds for quantum non-interactive correlation distillation

Abstract

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.