Quantum Information-theoretic Distance Metrics in Quantum Error Correction

Jincheng Zhang

Published Sep 3, 2026• 0 citations

Abstract

Quantum error correction (QEC) is a cornerstone of quantum information processing, aiming to protect fragile quantum information from decoherence and other noise sources. Traditional approaches to evaluating QEC code performance heavily rely on metrics like bit-error rate (BER), which provides a coarse-grained assessment. This paper proposes a novel framework for QEC performance evaluation utilizing information-theoretic distance measures. Specifically, we investigate the application of relative entropy (KL divergence) and other suitable distance functions to quantify the difference between the transmitted and received quantum states, offering a more nuanced and potentially more accurate measure of a code's performance. This approach allows for a deeper understanding of the code's resilience to specific types of errors. The core claim of this work is that information-theoretic distance metrics can improve the precision of QEC code assessments and guide the design of more effective codes. The mechanism involves leveraging the code's inherent error-correcting capability, coupled with the information-theoretic distance calculation, to evaluate and potentially refine the code parameters. We will explore the mathematical formulation of these distance measures and their application to various QEC codes.

DOI: 10.5281/zenodo.22273834

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