← Open problems
MUB-10.2
Show that no set of four MU bases exists when d = 6.
In plain terms
Zauner's conjecture in its d=6 form. Sufficient to settle the complete-set question.
Our position — ours alone, not the authors'
Our certified k=8 run is one slice of this: it shows no fourth MU basis accompanies any BH(6,8) class. That slice is Brierley-Weigert 2009 -- a reproduction, not a discovery. The full problem is far out of reach.
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