Entanglement-assisted quantum error-correcting codes from RS codes and BCH codes with extension degree 2

Galindo, Carlos; Hernando, Fernando; Ruano Benito, Diego

doi:10.1007/s11128-021-03101-4

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Título

Entanglement-assisted quantum error-correcting codes from RS codes and BCH codes with extension degree 2

Autor

Galindo, Carlos

Hernando, Fernando

Ruano Benito, Diego

Año del Documento

2021

Descripción

Producción Científica

Documento Fuente

Quantum Information Processing 20, 158 (2021)

Résumé

Entanglement-assisted quantum error correcting codes (EAQECCs) constructed from Reed-Solomon codes and BCH codes are considered in this work. It is provided a complete and explicit formula for the parameters of EAQECCs coming from any Reed-Solomon code, for the Hermitian metric, and from any BCH code with extension degree 2 and consecutive cyclotomic cosets, for both the Euclidean and the Hermitian metric. The main task in this work is the computation of a completely general formula for c, the minimum number of required maximally entangled quantum states.

ISSN

1570-0755

Revisión por pares

DOI

10.1007/s11128-021-03101-4

Patrocinador

This work was supported in part by the Spanish MICINN/FEDER grants PGC2018-096446-B-C21, PGC2018-096446-B-C22 and RED2018-102583-T, by the Spanish MINECO grant RYC-2016-20208 (AEI/FSE/UE), by the Junta de CyL (Spain) grant VA166G18, by the Generalitat Valenciana (Spain) grant AICO-2019-223 and by Universitat Jaume I grant P1-1B2018-10.

Version del Editor

https://doi.org/10.1007/s11128-021-03101-4