Two years ago, I blogged about Tuan-Yow Chien’s PhD thesis, which proved Zauner’s conjecture in dimension 17. The idea was to exploit certain conjectures on the field structure of SIC-POVM fiducial vectors so as to round numerical solutions to exact solutions. This week, the arXiv announced Chien’s latest paper (coauthored with Appleby, Flammia and Waldron), which extends this work to find exact solutions in 8 new dimensions.

The following line from the introduction caught my eye:

For instance the print-out for exact fiducial 48a occupies almost a thousand A4 pages (font size 9 and narrow margins).

As my previous blog entry illustrated, the description length of SIC-POVM fiducial vectors appears to grow rapidly with . However, it seems that the rate of growth is much better than I originally thought. Here’s a plot of the description lengths of the known fiducial vectors (the new ones due to ACFW17 — available here — appear in red):

Continue reading Zauner’s conjecture is true in dimensions 18, 20, 21, 30, 31, 37, 39 and 43