An algorithmic approach to entanglement-assisted quantum error-correcting codes from the Hermitian curve
René Bødker Christensen, Carlos Munuera, Francisco Revson F. Pereira, Diego Ruano, INFN, Sezione di Perugia, Via A. Pascoli, 06123 Perugia, Italy · Advances in Mathematics of Communications · 2022
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.