Further quantum designs
Beside MUBs (affine quantum designs, independent observables) and SIC POVMs
(quantum designs of degree 1) there exist (also in the case r=1) further
interesting special cases of quantum designs.
In the paper The finite Fourier Transform and projective 2-designs (arXiv: 2207.09922) (external link)
it is shown, that for or prime dimensions d= 3 (mod 4) an eigenvector basis of the Fourier Matrix exists, such that by applying the Weyl-Heisenberg
matrices to this, a projective 2-design is generated.
See also the according Powerpoint presentation
Download (pdf, 23 pages, 455 KB).
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