新纠缠辅助量子MDS码的构造

汪盼; 王立启; 朱士信

doi:10.12263/DZXB.20220819

您当前的位置：

首页 >

文章列表页 >

新纠缠辅助量子MDS码的构造

学术论文 | 更新时间：2026-04-10

- 新纠缠辅助量子MDS码的构造
- Construction of New Entanglement-Assisted Quantum MDS Codes
- 电子学报 2024年52卷第1期页码：288-297
- 作者机构：
  
  合肥工业大学数学学院，安徽合肥 230000
- 作者简介：
  
  [ "汪盼女，1997年生，安徽安庆人.合肥工业大学数学学院硕士研究生.研究方向为代数编码. E-mail: panwang_hfut@163.com" ]
  [ "王立启男，1986年生，安徽六安人.合肥工业大学数学学院副教授、硕士生导师.研究方向为代数编码. E-mail: liqiwangg@163.com" ]
  [ "朱士信男，1962年生，安徽枞阳人.合肥工业大学数学学院教授、博士生导师.研究方向为代数编码、序列密码与信息安全研究. E-mail: zhushixin@hfut.edu.cn" ]
- 基金信息：
  
  国家自然科学基金(12271137;U21A20428;12171134)
- DOI：10.12263/DZXB.20220819
  中图分类号： O157.4;TN911.22
- 收稿：2022-07-14，
  
  修回：2022-10-24，
  
  纸质出版：2024-01-25
- 稿件说明：
移动端阅览
汪盼,王立启,朱士信.新纠缠辅助量子MDS码的构造[J].电子学报,2024,52(01):288-297.

WANG Pan,WANG Li-qi,ZHU Shi-xin.Construction of New Entanglement-Assisted Quantum MDS Codes[J].ACTA ELECTRONICA SINICA,2024,52(01):288-297.
汪盼,王立启,朱士信.新纠缠辅助量子MDS码的构造[J].电子学报,2024,52(01):288-297. DOI： 10.12263/DZXB.20220819.

WANG Pan,WANG Li-qi,ZHU Shi-xin.Construction of New Entanglement-Assisted Quantum MDS Codes[J].ACTA ELECTRONICA SINICA,2024,52(01):288-297. DOI： 10.12263/DZXB.20220819.

摘要

纠缠辅助量子纠错码是经典量子纠错码的推广，通过在接收者和发送者双方预先共享纠缠态的方式实现量子通信.由于预先共享纠缠态会造成额外的费用，如何构造具有较小预先共享纠缠态的纠缠辅助量子纠错码是一个有趣的问题.本文给出了有限域

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=56706496&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=56706493&type=

3.64066648

3.47133350

上一类负循环码是厄米特对偶包含码的充分条件，通过研究其分圆陪集的结构性质，确定了不同数目的预先共享纠缠态的存在条件，并结合纠缠辅助量子纠错码的构造方法，构造了一些新的具有较小预先共享纠缠态的纠缠辅助量子Maximum-Distance-Separable（MDS）码.

Abstract

Entanglement-assisted quantum error-correcting codes are the generalization of classical quantum error-correcting codes

which realize quantum communication by using pre-shared entangled states between the receiver and the sender. It is an interesting problem to construct entanglement-assisted quantum error-correcting codes with small pre-shared entangled states because of the extra cost of pre-shared entangled states. In this paper

a sufficient condition for a class of negacyclic codes over finite fields to be Hermitian dual-containing codes is given. Then based on the structural properties of cyclotomic cosets

the existence conditions of different number of pre-shared entangled states are determined

and some new entanglement-assisted quantum maximum-distance-separable (MDS) codes with small pre-shared entangled states are obtained by using the construction method of entanglement-assisted quantum error-correcting codes.

关键词

Keywords

references

CALDERBANK A R , RAINS E M , SHOR P M , et al . Quantum error correction via codes over GF(4) [J]. IEEE Transactions on Information Theory , 1998 , 44 ( 4 ): 1369 - 1387 .

BRUN T , DEVETAK I , HSIEH M H . Correcting quantum errors with entanglement [J]. Science , 2006 , 314 ( 5798 ): 436 - 439 .

FAN J H , CHEN H W , XU J A . Constructions of q-ary entanglement-assisted quantum MDS codes with minimum distance greater than q+1 [J]. Quantum Information and Computation , 2016 , 16 ( 5&6 ): 423 - 434 .

LI L Q , ZHU S X , LIU L , et al . Entanglement-assisted quantum MDS codes from generalized Reed-Solomon codes [J]. Quantum Information Processing , 2019 , 18 ( 5 ): 1 - 15 .

李瑞虎 , 许根 , 吕良东 . BCH码的定义集分解及应用 [J]. 空军工程大学学报(自然科学版) , 2013 , 14 ( 2 ): 86 - 89 .

LI R H , XU G , LÜ L D . Decomposition of defining sets of BCH codes and its applications [J]. Journal of Air Force Engineering University (Natural Science Edition) , 2013 , 14 ( 2 ): 86 - 89 . (in Chinese)

GUENDA K , JITMAN S , GULLIVER T A . Constructions of good entanglement-assisted quantum error correcting codes [J]. Designs, Codes and Cryptography , 2018 , 86 ( 1 ): 121 - 136 .

LUO G J , CAO X W , CHEN X J . MDS codes with hulls of arbitrary dimensions and their quantum error correction [J]. IEEE Transactions on Information Theory , 2019 , 65 ( 5 ): 2944 - 2952 .

FANG W J , FU F W , LI L Q , et al . Euclidean and Hermitian hulls of MDS codes and their applications to EAQECCs [J]. IEEE Transactions on Information Theory , 2020 , 66 ( 6 ): 3527 - 3537 .

GAO Y Y , YUE Q , HUANG X M , et al . Hulls of generalized Reed-Solomon codes via Goppa codes and their applications to quantum codes [J]. IEEE Transactions on Information Theory , 2021 , 67 ( 10 ): 6619 - 6626 .

CAO M . MDS codes with Galois hulls of arbitrary dimensions and the related entanglement-assisted quantum error correction [J]. IEEE Transactions on Information Theory , 2021 , 67 ( 12 ): 7964 - 7984 .

LÜ L D , LI R H . Entanglement-assisted quantum codes constructed from primitive quaternary BCH codes [J]. International Journal of Quantum Information , 2014 , 12 ( 3 ): 1450015 .

LU L D , LI R H , GUO L B , et al . Entanglement-assisted quantum MDS codes from negacyclic codes [J]. Quantum Information Processing , 2018 , 17 ( 3 ): 69 .

CHEN J Z , HUANG Y Y , FENG C H , et al . Entanglement-assisted quantum MDS codes constructed from negacyclic codes [J]. Quantum Information Processing , 2017 , 16 ( 12 ): 303 .

QIAN J F , ZHANG L N . Constructions of new entanglement-assisted quantum MDS and almost MDS codes [J]. Quantum Information Processing , 2019 , 18 ( 3 ): 1 - 12 .

KOROGLU M E . New entanglement-assisted MDS quantum codes from constacyclic codes [J]. Quantum Information Processing , 2019 , 18 ( 2 ): 1 - 28 .

SARı M , KOLOTOĞLU E . An application of constacyclic codes to entanglement-assisted quantum MDS codes [J]. Computational and Applied Mathematics , 2019 , 38 ( 2 ): 75 .

LI R H , GUO G M , SONG H , et al . New constructions of entanglement-assisted quantum MDS codes from negacyclic codes [J]. International Journal of Quantum Information , 2019 , 17 ( 3 ): 1950022 .

LIU Y , LI R H , LV L D , et al . Application of constacyclic codes to entanglement-assisted quantum maximum distance separable codes [J]. Quantum Information Processing , 2018 , 17 ( 8 ): 210 .

LU L D , MA W P , GUO L B . Two families of entanglement-assisted quantum MDS codes from constacyclic codes [J]. International Journal of Theoretical Physics , 2020 , 59 : 1657 - 1667 .

WANG J L , LI R H , LV J J , et al . Entanglement-assisted quantum codes from cyclic codes and negacyclic codes [J]. Quantum Information Processing , 2020 , 19 : 138 .

WANG L Q , ZHU S X , SUN Z H . Entanglement-assisted quantum MDS codes from cyclic codes [J]. Quantum Information Processing , 2020 , 19 ( 2 ): 1 - 18 .

MACWILLIAMS F J , SLOANE N J A . The Theory of Error Correcting Codes [M]. Amsterdam : North-Holland Pub. Co. , 1977 .

LI R H , ZOU F , LIU Y , et al . Hermitian dual containing BCH codes and construction of new quantum codes [J]. Quantum Information and Computation , 2013 , 13 ( 1&2 ): 21 - 35 .

浏览量

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

暂无数据