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 proceedingConference contributionAcademicpeer-review

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.

LanguageEnglish
Title of host publication2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
Pages2559-2563
Number of pages5
ISBN (Electronic)9781538692912
DOIs
StatePublished - 1 Jul 2019
Event2019 IEEE International Symposium on Information Theory, ISIT 2019 - Paris, France
Duration: 7 Jul 201912 Jul 2019

Conference

Conference2019 IEEE International Symposium on Information Theory, ISIT 2019
CountryFrance
CityParis
Period7/07/1912/07/19

Fingerprint

Entanglement
Towers
Error-correcting Codes
Redundancy
Algebraic-geometry Codes
Geometry
Algebraic Function Fields
Decoherence
Quantum Systems
Family

Keywords

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

Cite this

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). [8849685] Piscataway: Institute of Electrical and Electronics Engineers. DOI: 10.1109/ISIT.2019.8849685
Pereira, Francisco R.F. ; Pellikaan, Ruud ; La Guardia, Giuliano G. ; De Assis, Francisco M./ Application of complementary dual AG codes to entanglement-assisted quantum codes. 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings. Piscataway : Institute of Electrical and Electronics Engineers, 2019. pp. 2559-2563
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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. DOI: 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.; De Assis, Francisco M.

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 proceedingConference contributionAcademicpeer-review

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Pereira FRF, Pellikaan R, La Guardia GG, De Assis FM. Application of complementary dual AG codes to entanglement-assisted quantum codes. In 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings. Piscataway: Institute of Electrical and Electronics Engineers. 2019. p. 2559-2563. 8849685. Available from, DOI: 10.1109/ISIT.2019.8849685