Asymmetric Entanglement-Assisted Quantum Error-Correcting Codes and BCH Codes
The concept of asymmetric entanglement-assisted quantum error-correcting code (asymmetric EAQECC) is introduced in this article. Codes of this type take advantage of the asymmetry in quantum errors since phase-shift errors are more probable than qudit-flip errors. Moreover, they use pre-shared entan...
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doaj-41dea9c11d8641259f32113787955e562021-06-15T23:00:21ZengIEEEIEEE Access2169-35362020-01-018185711857910.1109/ACCESS.2020.29674268962087Asymmetric Entanglement-Assisted Quantum Error-Correcting Codes and BCH CodesCarlos Galindo0https://orcid.org/0000-0002-3908-4462Fernando Hernando1https://orcid.org/0000-0002-9758-2152Ryutaroh Matsumoto2https://orcid.org/0000-0002-5085-8879Diego Ruano3https://orcid.org/0000-0001-7304-0087Departamento de Matemáticas, Instituto Universitario de Matemáticas y Aplicaciones de Castellón, Universitat Jaume I, Castellón de la Plana, SpainDepartamento de Matemáticas, Instituto Universitario de Matemáticas y Aplicaciones de Castellón, Universitat Jaume I, Castellón de la Plana, SpainDepartment of Information and Communication Engineering, Nagoya University, Nagoya, JapanIMUVA-Mathematics Research Institute, University of Valladolid, Valladolid, SpainThe concept of asymmetric entanglement-assisted quantum error-correcting code (asymmetric EAQECC) is introduced in this article. Codes of this type take advantage of the asymmetry in quantum errors since phase-shift errors are more probable than qudit-flip errors. Moreover, they use pre-shared entanglement between encoder and decoder to simplify the theory of quantum error correction and increase the communication capacity. Thus, asymmetric EAQECCs can be constructed from any pair of classical linear codes over an arbitrary field. Their parameters are described and a Gilbert-Varshamov bound is presented. Explicit parameters of asymmetric EAQECCs from BCH codes are computed and examples exceeding the introduced Gilbert-Varshamov bound are shown.https://ieeexplore.ieee.org/document/8962087/Asymmetric entanglement-assisted quantum error-correcting codesasymmetric entanglement-assisted Gilbert-Varshamov boundBCH codes |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Carlos Galindo Fernando Hernando Ryutaroh Matsumoto Diego Ruano |
spellingShingle |
Carlos Galindo Fernando Hernando Ryutaroh Matsumoto Diego Ruano Asymmetric Entanglement-Assisted Quantum Error-Correcting Codes and BCH Codes IEEE Access Asymmetric entanglement-assisted quantum error-correcting codes asymmetric entanglement-assisted Gilbert-Varshamov bound BCH codes |
author_facet |
Carlos Galindo Fernando Hernando Ryutaroh Matsumoto Diego Ruano |
author_sort |
Carlos Galindo |
title |
Asymmetric Entanglement-Assisted Quantum Error-Correcting Codes and BCH Codes |
title_short |
Asymmetric Entanglement-Assisted Quantum Error-Correcting Codes and BCH Codes |
title_full |
Asymmetric Entanglement-Assisted Quantum Error-Correcting Codes and BCH Codes |
title_fullStr |
Asymmetric Entanglement-Assisted Quantum Error-Correcting Codes and BCH Codes |
title_full_unstemmed |
Asymmetric Entanglement-Assisted Quantum Error-Correcting Codes and BCH Codes |
title_sort |
asymmetric entanglement-assisted quantum error-correcting codes and bch codes |
publisher |
IEEE |
series |
IEEE Access |
issn |
2169-3536 |
publishDate |
2020-01-01 |
description |
The concept of asymmetric entanglement-assisted quantum error-correcting code (asymmetric EAQECC) is introduced in this article. Codes of this type take advantage of the asymmetry in quantum errors since phase-shift errors are more probable than qudit-flip errors. Moreover, they use pre-shared entanglement between encoder and decoder to simplify the theory of quantum error correction and increase the communication capacity. Thus, asymmetric EAQECCs can be constructed from any pair of classical linear codes over an arbitrary field. Their parameters are described and a Gilbert-Varshamov bound is presented. Explicit parameters of asymmetric EAQECCs from BCH codes are computed and examples exceeding the introduced Gilbert-Varshamov bound are shown. |
topic |
Asymmetric entanglement-assisted quantum error-correcting codes asymmetric entanglement-assisted Gilbert-Varshamov bound BCH codes |
url |
https://ieeexplore.ieee.org/document/8962087/ |
work_keys_str_mv |
AT carlosgalindo asymmetricentanglementassistedquantumerrorcorrectingcodesandbchcodes AT fernandohernando asymmetricentanglementassistedquantumerrorcorrectingcodesandbchcodes AT ryutarohmatsumoto asymmetricentanglementassistedquantumerrorcorrectingcodesandbchcodes AT diegoruano asymmetricentanglementassistedquantumerrorcorrectingcodesandbchcodes |
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1721375694789804032 |