Construction of EAQECCs with imperfect ebits

• URL: http://arxiv.org/abs/2605.23119v1
• Date: Fri, 22 May 2026 00:42:55 GMT
• Title: Construction of EAQECCs with imperfect ebits
• Abstract summary: We generalize stabilizer formalism for entanglement-assisted quantum error-correcting codes with noisy ebits to EAQECCs-Ne.<n>Our results demonstrate that the proposed EAQECCs-Ne can outperform standard stabilizer codes with equivalent error-correcting capability.
• Score: 1.9336815376402718
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We generalize the stabilizer formalism for entanglement-assisted quantum error-correcting codes with noisy ebits (EAQECCs-Ne) from the binary case to the general $q$-ary case, where $q$ is a prime power. By leveraging the structure of the generalized Pauli group over $\mathbb{F}_q$ and symplectic geometry over $\mathbb{F}_q^{2n}$, we establish a unified framework for constructing EAQECCs-Ne for qudit systems. Equivalent formulations in terms of symplectic geometry over $\mathbb{F}_q$ and additive codes over $\mathbb{F}_q^{2n}$ are derived. We further construct several families of $q$-ary EAQECCs with noise ebits and analyze their performance compared to optimal stabilizer codes. Our results demonstrate that under certain noise conditions, the proposed EAQECCs-Ne can outperform standard stabilizer codes with equivalent error-correcting capability, offering a promising approach for fault-tolerant quantum computation in high-dimensional quantum systems.

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