河北师范大学学报—

期刊信息

刊名：河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
主办：河北师范大学
ISSN： 1000-5854
CN： 13-1061/N
中国科技核心期刊
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两体系统上的无偏不可扩展最大纠缠基

姬鹏飞^1,2

左会娟¹

(1.河北师范大学数学科学学院，河北石家庄 050024； 2.中国人民解放军陆军步兵学院石家庄校区，河北石家庄 050083)
DOI： 10.13763/j.cnki.jhebnu.nse.202601008

Constructions of mutually unbiased unextendible maximally entangled bases

Ji Pengfei^1,2,Zuo Huijuan¹

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摘要/Abstract

摘要：

量子纠缠在量子计算与量子信息处理中扮演着关键角色,然而其内在性质与数学结构至今尚未得到完整的刻画.相互无偏性作为描述量子纠缠的重要工具之一,近年来受到广泛关注.基于傅里叶矩阵和组合构型，在两体量子系统C^d⊗C^d′（d < d′）构造出两组相互无偏的不可扩展最大纠缠基,其中d′是奇素数.

Abstract：

Quantum entanglement plays a crucial role in quantum computing and quantum information processing. However, its intrinsic nature and mathematical structure have not yet been fully characterized. Mutual unbiasedness,as one of the important tools for describing quantum entanglement, has received widespread attention in recent years. Based on Fourier matrices,we construct two sets of mutually unbiased unextendible maximally entangled biased in bipartite quantum systems C^d⊗C^d′（d < d′）, where d′ is an odd prime number.

关键词

关键词： 两体量子系统；傅里叶矩阵；施密特系数；不可扩展最大纠缠基；相互无偏基

Key words： bipartite quantum systems ; Fourier matrices ; Schmidt number ; unextendible maximally entangled bases ; mutually unbiased bases

参考文献 20

[1] Aschbacher M,Childs A M,Wocjan P.The limitations of nice mutually unbiased bases[J].Journal of Algebraic Combinatorics,2007,25(2):111-123.DOI:10.1007/s10801-006-0002-y.
[2] Xiong Z X,Zheng Z J,Fei S M.Mutually unbiased unextendible maximally entangled bases in some systems of higher dimension[J].Quantum Information Processing,2020,19(12):429.DOI:10.1007/s11128-020-02923-y.
[3] Zhao H,Zhang L,Fei S M,et al.Constructing mutually unbiased bases from unextendible maximally entangled bases[J].Reports on Mathematical Physics,2020,85(1):105-118.DOI:10.1016/S0034-4877(20)30013-6.
[4] Zhang J,Tao Y H,Nan H,et al.Construction of mutually unbiased bases in CdC2ld′[J].Quantum Information Processing,2015,14(7):2635-2644.DOI:10.1007/s11128-015-0961-9.
[5] Nizamidin H,Ma T,Fei S M.A note on mutually unbiased unextendible maximally entangled bases in C2C3[J].International Journal of Theoretical Physics,2015,54(1):326-333.DOI:10.1007/s10773-014-2227-1.
[6] Nan H,Tao Y H,Li L S,et al.Unextendible maximally entangled bases and mutually unbiased bases in CdCd′[J].International Journal of Theoretical Physics,2015,54(3):927-932.DOI:10.1007/s10773-014-2288-1.
[7] Li M S,Wang Y L,Zheng Z J.Unextendible maximally entangled bases in CdCd′[J].Physical Review A,2014,89(6):062313.DOI:10.1103/physreva.89.062313.
[8] Wang Y L,Li M S,Fei S M,et al.Connecting unextendible maximally entangled base with partial Hadamard matrices[J].Quantum Information Processing,2017,16(3):84.DOI:10.1007/s11128-017-1537-7.
[9] Guo Y.Constructing the unextendible maximally entangled basis from the maximally entangled basis[J].Physical Review A,2016,94(5):052302.DOI:10.1103/physreva.94.052302.
[10] Wang Y L,Li M S,Fei S M.Unextendible maximally entangled bases in CdCd[J].Physical Review A,2014,90(3):034301.DOI:10.1103/physreva.90.034301.
[11] Chen B,Fei S M.Unextendible maximally entangled bases and mutually unbiased bases[J].Physical Review A,2013,88(3):034301.DOI:10.1103/physreva.88.034301.
[12] Bravyi S,Smolin J A.Unextendible maximally entangled bases[J].Physical Review A,2011,84(4):042306.DOI:10.1103/physreva.84.042306.
[13] Brierley S,Weigert S,Bengtsson I.All mutually unbiased bases in dimensions two to five[J].Quantum Information & Computation,2010,10(9):803-820.DOI:10.5555/2011464.2011470.
[14] Wootters W K,Fields B D.Optimal state-determination by mutually unbiased measurements[J].Annals of Physics,1989,191(2):363-381.DOI:10.1016/0003-4916(89)90322-9.
[15] Ivonovic I D.Geometrical description of quantal state determination[J].Journal of Physics A:Mathematical and General,1981,14(12):3241.DOI:10.1088/0305-4470/14/12/019.
[16] Spengler C,Huber M,Brierley S,et al.Entanglement detection via mutually unbiased bases[J].Physical Review A,2012,86(2):022311.DOI:10.1103/physreva.86.022311.
[17] Revzen M.Maximally entangled states via mutual unbiased collective bases[J].Physical Review A,2010,81:012113.DOI:10.1103/physreva.81.012113.
[18] Cerf N J,Bourennane M,Karlsson A,et al.Security of quantum key distribution using d-level systems[J].Physical Review Letters,2002,88(12):127902.DOI:10.1103/physrevlett.88.127902.
[19] Calderbank A R,Rains E M,Shor P W,et al.Quantum error correction and orthogonal geometry[J].Physical Review Letters,1997,78(3):405-408.DOI:10.1103/physrevlett.78.405.
[20] Bru D,Macchiavello C.Optimal eavesdropping in cryptography with three-dimensional quantum states[J].Physical Review Letters,2002,88(12):127901.DOI:10.1103/physrevlett.88.127901.