A FOURIER ANALYTIC APPROACH TO THE PROBLEM OF MUTUALLY UNBIASED BASES

被引：6
作者：
Matolcsi, Mate [1 ]
机构：
[1] Hungarian Acad Sci, Alfred Renyi Inst Math, H-1364 Budapest, Hungary
来源：
STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA | 2012年 / 49卷 / 04期
关键词：
Mutually unbiased bases; complex Hadamard matrices; difference sets; Delsarte's method; COMPLEX HADAMARD-MATRICES; STATE DETERMINATION; ORDER; 6; BOUNDS; DIMENSIONS;
D O I：
10.1556/SScMath.49.2012.4.1221
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give a new approach to the problem of mutually unbiased bases (MUBs), based on a Fourier analytic technique borrowed from additive combinatorics. The method provides a short and elegant generalization of the fact that there are at most d + 1 MUBs in C-d. It may also yield a proof that no complete system of MUBs exists in some composite dimensions - a long standing open problem.
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收藏
页码：482 / 491
页数：10
相关论文
共 31 条
  • [1] A new proof for the existence of mutually unbiased bases
    Bandyopadhyay, S
    Boykin, PO
    Roychowdhury, V
    Vatan, F
    [J]. ALGORITHMICA, 2002, 34 (04) : 512 - 528
  • [2] Orthogonal maximal abelian *-subalgebras of the 6x6 matrices
    Beauchamp, Kyle
    Nicoara, Remus
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2008, 428 (8-9) : 1833 - 1853
  • [3] Belovs A, 2008, LECT NOTES COMPUT SC, V5393, P50, DOI 10.1007/978-3-540-89994-5_6
  • [4] Mutually unbiased bases and Hadamard matrices of order six
    Bengtsson, Ingemar
    Bruzda, Wojciech
    Ericsson, Asa
    Larsson, Jan-Ake
    Tadej, Wojciech
    Zyczkowski, Karol
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 2007, 48 (05)
  • [5] Boykin PO, 2007, QUANTUM INF COMPUT, V7, P371
  • [6] BRIERLEY S., J PHYS C SER, V254
  • [7] Brierley S, 2010, QUANTUM INF COMPUT, V10, P803
  • [8] Maximal sets of mutually unbiased quantum states in dimension 6
    Brierley, Stephen
    Weigert, Stefan
    [J]. PHYSICAL REVIEW A, 2008, 78 (04):
  • [9] Constructing mutually unbiased bases in dimension six
    Brierley, Stephen
    Weigert, Stefan
    [J]. PHYSICAL REVIEW A, 2009, 79 (05):
  • [10] Numerical evidence for the maximum number of mutually unbiased bases in dimension six
    Butterley, Paul
    Hall, William
    [J]. PHYSICS LETTERS A, 2007, 369 (1-2) : 5 - 8
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