← Open problems
MUB-10.7
Can one improve the lower bound provided in Thm. 6.1, to find larger sets of MU bases in composite dimensions?
In plain terms
For d = 2p the known constructions yield only three MU bases no matter how large d gets. A constructive question -- a YES needs one object.
Our position — ours alone, not the authors'
Witness-shaped, which fits our bias toward chasing a YES. But the search space is a continuous manifold, not a finite grid, so our SAT machinery does not apply and our algebraic machinery has no finite ideal to chew.
Source
Daniel McNulty, Stefan Weigert, Mutually Unbiased Bases in Composite Dimensions -- A Review
Quantum 10, 2051 (2026) · §10.3
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