Quantum data processing and error correction

TL;DR

This work introduces coherent information as a fundamental intrinsic measure of quantum information flow through noisy channels, alongside entanglement fidelity and entropy production. By employing purification with a reference system and unitary dilations with an environment, it derives a quantum data processing inequality showing that coherent information cannot increase under sequential processing. It further proves that perfect quantum error correction is possible if and only if the input entropy equals the channel's coherent information, meaning the environment gains no information about the state. Together, these results establish a quantum-information-theoretic framework that parallels classical mutual information while highlighting unique quantum features and time asymmetry, with direct implications for error correction and information security in quantum processes.

Abstract

This paper investigates properties of noisy quantum information channels. We define a new quantity called {\em coherent information} which measures the amount of quantum information conveyed in the noisy channel. This quantity can never be increased by quantum information processing, and it yields a simple necessary and sufficient condition for the existence of perfect quantum error correction.