Application of complementary dual AG codes to entanglement-assisted quantum codes

Francisco R.F. Pereira; Ruud Pellikaan; Giuliano G. La Guardia; Francisco M. De Assis

doi:10.1109/ISIT.2019.8849685

Application of complementary dual AG codes to entanglement-assisted quantum codes

Francisco R.F. Pereira
, Ruud Pellikaan
, Giuliano G. La Guardia
, Francisco M. De Assis

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

6 Citaten (Scopus)

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Quantum error correcting codes play the role of suppressing noise and decoherence in quantum systems by introducing redundancy. Some strategies can be used to improve the parameters of these codes. For example, entanglement can provide a way for quantum error correcting codes to achieve higher rates than the one obtained via traditional stabilizer formalism. Such codes are called entanglement-assisted quantum (QUENTA) codes. In this paper, we use algebraic geometry codes to construct two families of QUENTA codes, where one of them has maximal entanglement and is maximal distance separable. In the end, we show that for any asymptotically good tower of algebraic function fields there is an asymptotically good family of maximal entanglement QUENTA codes with nonzero rate, relative minimal distance, and relative amount of entanglement.

Originele taal-2	Engels
Titel	2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
Plaats van productie	Piscataway
Uitgeverij	Institute of Electrical and Electronics Engineers
Pagina's	2559-2563
Aantal pagina's	5
ISBN van elektronische versie	9781538692912
DOI's	https://doi.org/10.1109/ISIT.2019.8849685
Status	Gepubliceerd - 1 jul. 2019
Evenement	2019 IEEE International Symposium on Information Theory, ISIT 2019 - Paris, Frankrijk Duur: 7 jul. 2019 → 12 jul. 2019

Congres

Congres	2019 IEEE International Symposium on Information Theory, ISIT 2019
Land/Regio	Frankrijk
Stad	Paris
Periode	7/07/19 → 12/07/19

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10.1109/ISIT.2019.8849685

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Pereira, F. R. F., Pellikaan, R., La Guardia, G. G., & De Assis, F. M. (2019). Application of complementary dual AG codes to entanglement-assisted quantum codes. In 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings (blz. 2559-2563). Artikel 8849685 Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/ISIT.2019.8849685

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title = "Application of complementary dual AG codes to entanglement-assisted quantum codes",

abstract = "Quantum error correcting codes play the role of suppressing noise and decoherence in quantum systems by introducing redundancy. Some strategies can be used to improve the parameters of these codes. For example, entanglement can provide a way for quantum error correcting codes to achieve higher rates than the one obtained via traditional stabilizer formalism. Such codes are called entanglement-assisted quantum (QUENTA) codes. In this paper, we use algebraic geometry codes to construct two families of QUENTA codes, where one of them has maximal entanglement and is maximal distance separable. In the end, we show that for any asymptotically good tower of algebraic function fields there is an asymptotically good family of maximal entanglement QUENTA codes with nonzero rate, relative minimal distance, and relative amount of entanglement.",

keywords = "Algebraic Geometry Codes, Asymptotically Good, Maximal Distance Separable, Maximal Entanglement, Quantum Codes",

author = "Pereira, \{Francisco R.F.\} and Ruud Pellikaan and \{La Guardia\}, \{Giuliano G.\} and \{De Assis\}, \{Francisco M.\}",

year = "2019",

month = jul,

day = "1",

doi = "10.1109/ISIT.2019.8849685",

language = "English",

pages = "2559--2563",

booktitle = "2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings",

publisher = "Institute of Electrical and Electronics Engineers",

address = "United States",

note = "2019 IEEE International Symposium on Information Theory, ISIT 2019 ; Conference date: 07-07-2019 Through 12-07-2019",

}

Pereira, FRF, Pellikaan, R, La Guardia, GG & De Assis, FM 2019, Application of complementary dual AG codes to entanglement-assisted quantum codes. in 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings., 8849685, Institute of Electrical and Electronics Engineers, Piscataway, blz. 2559-2563, 2019 IEEE International Symposium on Information Theory, ISIT 2019, Paris, Frankrijk, 7/07/19. https://doi.org/10.1109/ISIT.2019.8849685

Application of complementary dual AG codes to entanglement-assisted quantum codes. / Pereira, Francisco R.F.; Pellikaan, Ruud; La Guardia, Giuliano G. et al.
2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings. Piscataway: Institute of Electrical and Electronics Engineers, 2019. blz. 2559-2563 8849685.

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

TY - GEN

T1 - Application of complementary dual AG codes to entanglement-assisted quantum codes

AU - Pereira, Francisco R.F.

AU - Pellikaan, Ruud

AU - La Guardia, Giuliano G.

AU - De Assis, Francisco M.

PY - 2019/7/1

Y1 - 2019/7/1

N2 - Quantum error correcting codes play the role of suppressing noise and decoherence in quantum systems by introducing redundancy. Some strategies can be used to improve the parameters of these codes. For example, entanglement can provide a way for quantum error correcting codes to achieve higher rates than the one obtained via traditional stabilizer formalism. Such codes are called entanglement-assisted quantum (QUENTA) codes. In this paper, we use algebraic geometry codes to construct two families of QUENTA codes, where one of them has maximal entanglement and is maximal distance separable. In the end, we show that for any asymptotically good tower of algebraic function fields there is an asymptotically good family of maximal entanglement QUENTA codes with nonzero rate, relative minimal distance, and relative amount of entanglement.

AB - Quantum error correcting codes play the role of suppressing noise and decoherence in quantum systems by introducing redundancy. Some strategies can be used to improve the parameters of these codes. For example, entanglement can provide a way for quantum error correcting codes to achieve higher rates than the one obtained via traditional stabilizer formalism. Such codes are called entanglement-assisted quantum (QUENTA) codes. In this paper, we use algebraic geometry codes to construct two families of QUENTA codes, where one of them has maximal entanglement and is maximal distance separable. In the end, we show that for any asymptotically good tower of algebraic function fields there is an asymptotically good family of maximal entanglement QUENTA codes with nonzero rate, relative minimal distance, and relative amount of entanglement.

KW - Algebraic Geometry Codes

KW - Asymptotically Good

KW - Maximal Distance Separable

KW - Maximal Entanglement

KW - Quantum Codes

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U2 - 10.1109/ISIT.2019.8849685

DO - 10.1109/ISIT.2019.8849685

M3 - Conference contribution

AN - SCOPUS:85073157332

SP - 2559

EP - 2563

BT - 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings

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T2 - 2019 IEEE International Symposium on Information Theory, ISIT 2019

Y2 - 7 July 2019 through 12 July 2019

ER -

Application of complementary dual AG codes to entanglement-assisted quantum codes

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