Quantum resource theory of coding for error correction

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, incl...

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Bibliographic Details
Published in:arXiv.org 2024-09
Main Authors: Dong-Sheng, Wang, Yuan-Dong, Liu, Yun-Jiang, Wang, Luo, Shunlong
Format: Article
Language:English
Subjects:
Coding
Data processing
Error correction
Fault tolerance
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2409.09416