A decoupling approach to classical data transmission over quantum channels

TL;DR

This paper introduces a decoupling-based method to transmit classical data over quantum channels, extending quantum Shannon theory techniques to the one-shot scenario and providing a new proof of the classical capacity theorem.

Contribution

It presents a novel decoupling approach to classical data transmission over quantum channels, including a dequantizing theorem and a one-shot generalization of the Holevo-Schumacher-Westmoreland Theorem.

Findings

Established a decoupling-based proof for classical communication over quantum channels.

Proved a dequantizing theorem ensuring classical correlation with the environment.

Generalized the Holevo-Schumacher-Westmoreland Theorem to one-shot scenarios.

Abstract

Most coding theorems in quantum Shannon theory can be proven using the decoupling technique: to send data through a channel, one guarantees that the environment gets no information about it; Uhlmann's theorem then ensures that the receiver must be able to decode. While a wide range of problems can be solved this way, one of the most basic coding problems remains impervious to a direct application of this method: sending classical information through a quantum channel. We will show that this problem can, in fact, be solved using decoupling ideas, specifically by proving a "dequantizing" theorem, which ensures that the environment is only classically correlated with the sent data. Our techniques naturally yield a generalization of the Holevo-Schumacher-Westmoreland Theorem to the one-shot scenario, where a quantum channel can be applied only once.