Gerhard Zauner

Below are files containing the fiducial vectors used for the calculations in the paper Galois Automorphisms of a Symmetric Measurement arXiv:1209.1813. For the definitions of the parameters a, r1, ..., t, b1, ... see the tables on pp.33 and 34 of that paper.

The fiducials are all unnormalized. Up to a normalization factor and a phase they are exact versions of the numerical fiducials with the same labelling as in the paper by A.J.Scott and M. Grassl arXiv:0910.5784 (except for dimension 8, where a different choice was made for the reasons explained in arXiv:1209.1813). They were obtained from previously known exact fiducials by first transforming them with the extended Clifford group operators tabulated on p.32 of arXiv:1209.1813, and then taking the first column of the corresponding projectors.

dimension d label fiducial
4 a d4a
5 a d5a
6 a d6a
7 a d7a
b d7b
8 a d8a
b d8b
9 a d9a
b d9b
10 a d10a
11 a d11a
b d11b
c d11c
12 a d12a
b d12b
13 a d13a
b d13b
14 a d14a
b d14b
15 d d15d
16 a d16a
b d16b
19 e d19e
24 c d24c
28 c d28c
35 j d35j
48 g d48g

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Copyright © 2010-2012 Gerhard Zauner