A remarkable representation of the Clifford group
Quantum Physics
2012-02-17 v1
Abstract
The finite Heisenberg group knows when the dimension of Hilbert space is a square number. Remarkably, it then admits a representation such that the entire Clifford group --- the automorphism group of the Heisenberg group --- is represented by monomial phase-permutation matrices. This has a beneficial influence on the amount of calculation that must be done to find Symmetric Informationally Complete POVMs. I make some comments on the equations obeyed by the absolute values of the components of the SIC vectors, and on the fact that the representation partly suggests a preferred tensor product structure.
Keywords
Cite
@article{arxiv.1202.3559,
title = {A remarkable representation of the Clifford group},
author = {Ingemar Bengtsson},
journal= {arXiv preprint arXiv:1202.3559},
year = {2012}
}
Comments
6 pages; talk at the Vaxjo conference on Advances in Quantum Theory, 2010