Entanglement-Assisted Codes Outside the Stabilizer Framework

2026-03-03

AI Summary

This study addresses the construction of entanglement-assisted quantum error-correcting codes within the non-stabilizer framework to enable reliable quantum communication in scenarios where noisy and noiseless entangled qubits coexist. The work proposes the first entanglement-assisted coding method applicable to non-stabilizer and non-codeword-stabilizer structures—including XP-stabilizer codes and permutation-invariant codes—by associating arbitrary quantum codes with subsets of physical qubits correctable under a quantum erasure channel. It reveals a fundamental trade-off between the compressibility of entangled states at the receiver and the error-correction capability in degenerate codes. By integrating entanglement distribution, compression techniques, and algebraic code design, the authors construct several new families of entanglement-assisted codes that significantly extend the theoretical boundaries of non-stabilizer coding while preserving communication performance.

Technology Category

• Machine Learning: Quantum Machine Learning
• Multiagent Systems: Agent Communication
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Assisted, interactive, and conversational search
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We show how entanglement-assisted codes can be constructed from arbitrary quantum codes by associating them with quantum codes for erasure channels. If a subset of physical qubits is correctable for an erasure error, then it naturally forms the receiver's share of a bipartite state that can be used for entanglement-assisted communications, both in the noiseless and noisy ebit error models. In the case of degenerate codes, we show that the receiver's share of the bipartite state can sometimes be compressed, at the cost of potentially reduced error-correction ability in the noisy ebit error model. We also give examples of permutation-invariant and XP-stabilizer entanglement-assisted codes, the first outside of the stabilizer and codeword-stabilized frameworks.

Problem

• entanglement-assisted codes
• quantum error correction
• erasure channels
• degenerate codes
• non-stabilizer codes

Innovation

• entanglement-assisted codes
• erasure channels
• degenerate codes
• permutation-invariant codes
• XP-stabilizer