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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

6 Citations (Scopus)

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.

Original language	English
Title of host publication	2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
Place of Publication	Piscataway
Publisher	Institute of Electrical and Electronics Engineers
Pages	2559-2563
Number of pages	5
ISBN (Electronic)	9781538692912
DOIs	https://doi.org/10.1109/ISIT.2019.8849685
Publication status	Published - 1 Jul 2019
Event	2019 IEEE International Symposium on Information Theory, ISIT 2019 - Paris, France Duration: 7 Jul 2019 → 12 Jul 2019

Conference

Conference	2019 IEEE International Symposium on Information Theory, ISIT 2019
Country/Territory	France
City	Paris
Period	7/07/19 → 12/07/19

Keywords

Algebraic Geometry Codes
Asymptotically Good
Maximal Distance Separable
Maximal Entanglement
Quantum Codes

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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 (pp. 2559-2563). Article 8849685 Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/ISIT.2019.8849685

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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.",

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

year = "2019",

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doi = "10.1109/ISIT.2019.8849685",

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

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

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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, pp. 2559-2563, 2019 IEEE International Symposium on Information Theory, ISIT 2019, Paris, France, 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. p. 2559-2563 8849685.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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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.

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KW - Asymptotically Good

KW - Maximal Distance Separable

KW - Maximal Entanglement

KW - Quantum Codes

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

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