Quantum Error Correction Coding and Information Entropy: A Unified Theory

Jincheng Zhang

Published Aug 28, 2026• 0 citations

Abstract

This paper presents a unified theoretical framework for quantum error correction coding and information entropy. The central argument posits that quantum error correction and information entropy represent fundamentally the same physical phenomenon. This relationship is described by a single mathematical structure. The theory leverages quantum phenomena like superposition and entanglement to develop an error correction scheme, where entanglement enhances resilience while the error correction process itself is viewed as a reduction in information entropy. The core of this work explores the deep connection between these previously distinct fields, offering new perspectives for quantum computation and information transmission. The primary mathematical tools employed are probability theory, information theory, and linear algebra. We define key parameters such as the entropy of a state, the fidelity of a quantum state, and the distance between states. The goal is to provide a cohesive understanding of the underlying mechanisms driving both error correction and the quantification of uncertainty in quantum systems. The theoretical framework presented here provides a novel approach to understanding and potentially optimizing quantum information processing.

DOI: 10.5281/zenodo.22137493

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