The Frame Potential, on Average
Quantum Physics
2009-08-26 v2
Abstract
A SIC consists of N^2 equiangular unit vectors in an N dimensional Hilbert space. The frame potential is a function of N^2 unit vectors. It has a unique global minimum if the vectors form a SIC, and this property has been made use of in numerical searches for SICs. When the vectors form an orbit of the Heisenberg group the frame potential becomes a function of a single fiducial vector. We analytically compute the average of this function over Hilbert space. We also compute averages when the fiducial vector is placed in certain special subspaces defined by the Clifford group.
Cite
@article{arxiv.0808.2947,
title = {The Frame Potential, on Average},
author = {Ingemar Bengtsson and Helena Granstrom},
journal= {arXiv preprint arXiv:0808.2947},
year = {2009}
}
Comments
15 pages. Major mistake corrected in version 2