A random-coding based proof for the quantum coding theorem

TL;DR

This paper provides a new proof of the quantum channel coding theorem using random coding arguments, showing that randomly chosen code spaces are effective for quantum error correction, similar to classical Shannon theory.

Contribution

It introduces a random-coding based proof for the quantum coding theorem, aligning quantum error correction with classical Shannon methods.

Findings

Randomly chosen code spaces are highly suitable for quantum error correction.

The proof parallels Shannon's classical information transmission approach.

Supports the effectiveness of random coding in quantum information theory.

Abstract

We present a proof for the quantum channel coding theorem which relies on the fact that a randomly chosen code space typically is highly suitable for quantum error correction. In this sense, the proof is close to Shannon's original treatment of information transmission via a noisy classical channel.