From SICs and MUBs to Eddington
Mathematical Physics
2015-05-27 v1 math.MP
Quantum Physics
Abstract
This is a survey of some very old knowledge about Mutually Unbiased Bases (MUB) and Symmetric Informationally Complete POVMs (SIC). In prime dimensions the former are closely tied to an elliptic normal curve symmetric under the Heisenberg group, while the latter are believed to be orbits under the Heisenberg group in all dimensions. In dimensions 3 and 4 the SICs are understandable in terms of elliptic curves, but a general statement escapes us. The geometry of the SICs in 3 and 4 dimensions is discussed in some detail.
Keywords
Cite
@article{arxiv.1103.2030,
title = {From SICs and MUBs to Eddington},
author = {Ingemar Bengtsson},
journal= {arXiv preprint arXiv:1103.2030},
year = {2015}
}
Comments
12 pages; from the Festschrift for Tony Sudbery