Entanglement-assisted quantum codes from algebraic geometry codes

Francisco Fernandes Pereira, Ruud Pellikaan, Giuliano Gadioli La Guardia, Francisco Marcos 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 three families of QUENTA codes, where one of them has maximal entanglement and is maximal distance separable. At 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 languageEnglish
Title of host publicationProceedings of the WCC 2019: The Eleventh International Workshop on Coding and Cryptography
Chapter33
Number of pages10
Publication statusPublished - 2019
EventThe Eleventh International Workshop on Coding and Cryptography - Saint-Jacut- de-la-Mer, France
Duration: 31 Mar 20195 Apr 2019
https://www.lebesgue.fr/content/sem2019-WCC

Conference

ConferenceThe Eleventh International Workshop on Coding and Cryptography
CountryFrance
CitySaint-Jacut- de-la-Mer
Period31/03/195/04/19
Internet address

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  • Cite this

    Fernandes Pereira, F., Pellikaan, R., Gadioli La Guardia, G., & de Assis, F. M. (2019). Entanglement-assisted quantum codes from algebraic geometry codes. In Proceedings of the WCC 2019: The Eleventh International Workshop on Coding and Cryptography