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An Algorithmic Approach to Entanglement-Assisted Quantum Error-Correcting Codes from the Hermitian Curve (2105.02166v2)
Published 5 May 2021 in cs.IT and math.IT
Abstract: We study entanglement-assisted quantum error-correcting codes (EAQECCs) arising from classical one-point algebraic geometry codes from the Hermitian curve with respect to the Hermitian inner product. Their only unknown parameter is $c$, the number of required maximally entangled quantum states since the Hermitian dual of an AG code is unknown. In this article, we present an efficient algorithmic approach for computing $c$ for this family of EAQECCs. As a result, this algorithm allows us to provide EAQECCs with excellent parameters over any field size.