SICPOVMs: A new computer study
Abstract
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 WeylHeisenberg 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.
 Publication:

arXiv eprints
 Pub Date:
 October 2009
 arXiv:
 arXiv:0910.5784
 Bibcode:
 2009arXiv0910.5784S
 Keywords:

 Quantum Physics;
 Mathematics  Combinatorics;
 Mathematics  Functional Analysis
 EPrint:
 20 pages + 189 pages of raw data (also accessible in the source in plain text files)