Quantum resource theory of coding for error correction

TL;DR

This paper develops a quantum resource theory framework for error correction, classifying various coding models as superchannels, which could lead to new error-correction strategies.

Contribution

It introduces a hierarchy of quantum coding models using superchannels, unifying different error correction and communication scenarios within a rigorous resource-theoretic approach.

Findings

Established a hierarchy of quantum coding models

Classified error-correction codes based on resource theory

Potential to inspire new coding and error-correction methods

Abstract

Error-correction codes are central for fault-tolerant information processing. Here we develop a rigorous framework to describe various coding models based on quantum resource theory of superchannels. We find, by treating codings as superchannels, a hierarchy of coding models can be established, including the entanglement assisted or unassisted settings, and their local versions. We show that these coding models can be used to classify error-correction codes and accommodate different computation and communication settings depending on the data type, side channels, and pre-/postprocessing. We believe the coding hierarchy could also inspire new coding models and error-correction methods.