Topological Redundancy in Quantum Entanglement Encoding

Jincheng Zhang

Published Sep 1, 2026• 0 citations

Abstract

This paper investigates the potential of incorporating topological redundancy into quantum entanglement encoding schemes. The core claim is that strategically designing quantum entanglement codes leveraging specific topological structures can significantly enhance the resilience of quantum entanglement, ultimately leading to more efficient quantum information transmission. This approach utilizes the topological protection effect, shielding entangled states from local perturbations by encoding them within the inherent topology of the system. Furthermore, topological redundancy allows for the reconstruction of complex entanglement networks using a limited number of entangled pairs. The theoretical framework presented here outlines the key principles and potential benefits of this novel approach, offering a pathway towards robust and scalable quantum technologies. We explore the mathematical underpinnings of this strategy, focusing on the encoding and decoding processes within the defined topological framework. The central equation governing the entanglement fidelity is: F = |⟨ψ|Φ⟩|2 where ψ represents the encoded state and Φ represents the measured state. The topological protection ensures that small perturbations will not significantly alter the state |ψ⟩, thus maintaining a high fidelity. The concept of topological redundancy is formalized as: R = Σi |ψi⟩⟨ψi| where ψi are the fundamental entangled states and R describes the overall redundant information. This redundancy allows for the reconstruction of more complex entangled states through appropriate combinations of the fundamental states. This work provides a foundational understanding for future research into topological quantum information processing.

DOI: 10.5281/zenodo.22223502

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