← Open problems
MUB-10.5
Find all pairs of 6 x 6 complex Hadamard matrices H1 and H2 such that their product H1-dagger H2 is another Hadamard matrix.
In plain terms
Equivalent to identifying all MU triples in d=6. Conjecture 8.1 proposes the Fourier family F6(2), its transpose, and Szollosi's X6(2) as the only candidates.
Our position — ours alone, not the authors'
Conjecture 8.1 names a FINITE candidate list, and checking named candidates is what our certificates do. Needs a desk gate first: the conjecture may already have been verified at the parameter points that matter.
Source
Daniel McNulty, Stefan Weigert, Mutually Unbiased Bases in Composite Dimensions -- A Review
Quantum 10, 2051 (2026) · §10.2
https://doi.org/10.22331/q-2026-04-01-2051
Licence:
CC-BY-4.0
— the problem statement is quoted here under that
licence, with attribution, and has not been modified