SIC-POVMs: A new computer study

Details SIC-POVMs: A new computer study SIC-POVMs: A new computer study

2009-10-30

arxiv.org/abs/0910.5784v2

J. Math. Phys. 51, 042203 (2010)

Physics

Quantum Physics

20 pages + 189 pages of raw data (also accessible in the source in plain text files); further algebraic solutions for d=11 and

Scientific paper

10.1063/1.3374022

We report on a new computer study into 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.

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