Symmetric informationally complete positive-operator-valued measures: A new computer study

被引：204
|
作者：
Scott, A. J. [1 ,2 ]
Grassl, M. [3 ]
机构：
[1] Griffith Univ, Ctr Quantum Comp Technol, Brisbane, Qld 4111, Australia
[2] Griffith Univ, Ctr Quantum Dynam, Brisbane, Qld 4111, Australia
[3] Natl Univ Singapore, Ctr Quantum Technol, Singapore 117543, Singapore
来源：
JOURNAL OF MATHEMATICAL PHYSICS | 2010年 / 51卷 / 04期
基金：
新加坡国家研究基金会; 澳大利亚研究理事会;
关键词：
EQUIANGULAR LINES; SIC-POVMS; FRAMES; BASES; ADVENT; SYSTEM; BOUNDS; LIFE;
D O I：
10.1063/1.3374022
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We report on a new computer study of the existence of d(2) equiangular lines in d complex dimensions. Such maximal complex projective codes are conjectured to exist in all finite dimensions and are the underlying mathematical objects defining symmetric informationally complete measurements in quantum theory. We provide numerical solutions in all dimensions d <= 67 and, moreover, a putatively complete list of Weyl-Heisenberg covariant solutions for d <= 50. A symmetry analysis of this list leads to new algebraic solutions in dimensions d=24, 35, and 48, which are given together with algebraic solutions for d=4,...,15, and 19. (C) 2010 American Institute of Physics. [doi:10.1063/1.3374022]
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页数：16
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