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arXiv · 2409.09416

Quantum resource theory of coding for error correction

Dong-Sheng Wang·Yuan-Dong Liu·Yun-Jiang Wang·Shunlong Luo
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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.

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Dong-Sheng Wang, Yuan-Dong Liu, Yun-Jiang Wang, Shunlong Luo. 2024-09-14. Quantum resource theory of coding for error correction. https://doi.org/10.1103/physreva.110.032413

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